Yes, Kessler Syndrome

In particular:

The Envisat satellite is a large, inactive satellite with a mass of 8,211 kg (18,102 lb) that drifts at 785 km (488 mi), an altitude where the debris environment is the greatest—two catalogued objects can be expected to pass within about 200 meters of Envisat every year—and likely to increase. It could easily become a major debris contributor from a collision during the next 150 years that it will remain in orbit.

It wouldn't be instantaneous but if you exploded a few suitable targets such as Envisat you could fill the relevant sections of space with destructive fragments that then cause a cascade of strikes into other targets. Space could become a very hostile environment in a few years and remain that way for decades.

All at once, none that I know of. But you can always count on the good old human party trick:

Blow it up

The classical Bond's movie move is to send a few dozens missiles and take down enough of the network to accomplish your goal. Let's take GPS, for reference. GPS work with geo-synchronous satellites broadcasting an universal time set on an atomic clock¹.
It it bothers you, skip that part:

Your device receive signals from those satellites that tell them when the satellite broadcasted it. It deduces the time each signal took to come from each satellite, thus allowing to triangulate your position (triangulate as in, you need at least 3 to pinpoint your position in space, otherwise, you end up with a sphere or a circle and it's not convenient).

What I'm getting at is that the system is highly dependent on its network. If you take out enough of the grid, you create at least a "no-service" zone (per Earth obscuration), or you make it completely ineffective.

My guess would be that a few missiles strikes would do quite a bit of damage to your satellite network. ¹ (Not sure which missiles are able to reach satellite orbit if any though. But it's well within our reach, as well as any sci-fi race bothering visiting us)

Other option:

EMP

This one is highly hypothetical and should be taken with lots of care. EMP (electro-magnetic pulse) is a common sci-fi trope. Basically, a very powerful electro magnetic field disrupt electronics, and it's pretty nasty on computers. I think I remember Call of Duty MWII² used a nuke exploding in orbit to disable satellites. Now, an explosion happening into the void of space does not end up in a big ball of fire a la Death Star. If I'm not mistaken, it instead produce electro magnetic radiation (among probably other things. I'm stressing ¹ on this point).

Thing is, radiations and electro magnetic fields are probably something to expect in space. (Radiation is a given, EMP... maybe ³). So I wouldn't be surprised if satellites were protected against natural causes for this. But it might be worth looking into the theory.

This answer does not support any kind of attempt to take down satellites and I hereby decline responsibility if anyone manage to make sense of this thoroughly uninformed ramble and somehow devise the weapons to enact it.

_{1: No expert here, anyone feel free to correct me if I misunderstood something / made a mistake.
2: See why I said lots of care? [sarcasm]Very reliable source for sure [/sarcasm]
3: I mean, I know there is electro magnetic radiation in space, as even Earth has an electromagnetic field. The thing is, I don't know if they are powerful enough to fry electronics. Slight disgression here, that would need to be answered by someone actually knowledgeable about this.}

Edit 1: As pointed in comments, I was mistaken about GPS using geo-synchronous satellites. Thanks to Zeiss Ikon and user71659 for their clarifications.⁴

Zeiss Ikon: "GPS are not geosynchronous. They're at 20,200 km, which is close to half of GEO height, and some are in highly inclined orbits rather than equatorial."

user71659: "GPS is designed to be difficult to blow up by having six separate orbital planes. [...] On top of that, there's literally more GPS satellites in orbit than the system can handle. The system needs 24, it can handle 31 at the same time, and there's 40 usable. The extras are simply on standby as spares. Compare that to GLONASS which is 1 away from losing global coverage and Galileo which 4 short for global coverage (delays & a launch mishap)."

It makes sense some network are designed to be robust since GPS was originally a military project under the name Navstar GPS. Including system redundancy is done precisely to counter-act the loss of a few satellites. If we follow user71659 comment, you'd need to blow up at least 17 satellites to impede the system (to which extent, I don't know).
user71659 also suggested geo comsats would be an easier target to disable. Unfortunately, I'd need a little disambiguation as a research results are numerous, so I suggest you ask directly our fellow terrorist.SE user.

Furthermore, the Kessler effect have been pointed out several times in other answers. I didn't include it in mine for two reasons.

First, I didn't know the name of the phenomenon at the time, though it would be an obvious byproduct of exploding satellites.

Second, satellites using differents orbits at differents altitudes, I suppose it would not be "just" blowing up some satellites and would requires some maths beforehand to ensure enough remaining orbital devices would be hit in an acceptable time-frame (before the lost ones are replaced). Probability is an hard mistress though, and she commands that, if a satellite and debris have a chance to collide, they eventually will.

_{4: Let's give credit where it's due.}

The most obvious solution is the high-altitude nuke. Watch this:
https://www.youtube.com/watch?v=KcTrOGS3TyE

Just to summarize: nuclear blast sends a lot of charged particles at hight speed away. Earth's magnetic field redirects that back-and-forth, and since moving charges means current, and alternating current induces current in wires, it kills a lot of sensitive electric stuff, including satellites, telephone lines, electric cables, and everything connected to the end of those. So there will be a lot of collateral damage, only use this if your story supports it.

A rocket armed with a grenade launcher and 2000 grenades

There are about 2000 satellites. Therefore, just make a rocket, launch it into space, and have it start firing grenades into each satellite individually. Satellites are designed to survive radiation and vacuums, not explosions. Apparently, they are structurally very fragile to save weight.

Note that you do not need to chase the satellites. That would take a lot of fuel. Instead, you can just aim the grenades at the satellites. There's (almost) no air resistance in space, so you can fire as far as your accuracy and precision permits.

If you got enough cash, you could even fire the grenades or even throw yourself. This would be a lot more expensive, since you need to launch a human into space and get a lot closer (since humans are not good at aiming), all on top of the tyranny of the rocket equation. That's a small price to pay to be the person to destroy all of Earth's satellites by dual-wielding grenade launchers though in space, in my opinion.

Both the US and old USSR had anti-satellite weapons in development before agreeing a treaty to play nice in space. I don't know if the results were ever considered viable weapons but I can't believe they would have deleted the blueprints. The Chinese actually shot at one of their own satellites a few years back.

So if we can do this now, then your postulated aliens with the technology to cross interstellar space should have no problems targeting a few thousand sittings ducks moving in well ordered and predictable orbits.

A shotgun makes a very capable weapon in orbit, with the advantage that the pellets don't fall to ground after 50m. If you can use laser, maser, emp/x-ray bursts or even old fashioned kinetic weapons it shouldn't be an impossible task. The magazine of the A-10 Thunderbolt carried 1350 rounds, so with perfect marksmanship you'd only need 4. Actually you could afford quite a few misses!

Some well-known hypotheticals:

• Have something crash into something to start the Kessler Syndrome.


• Build a big, ground-based laser or maser and start to take potshots at satellites. The US stopped Star Wars before it got there. The Chinese might have something like this.


• Come up with a set of malware to attack the ground control and to send destructive commands, like "spend all the maneuvering fuel get onto collision course with another sat." The problem, those control systems are rather hard.

I suppose if your aliens can cross light years of space, they might have some as-yet-unexplained way to cause a massive solar flare or coronal mass ejection.

A solar flare is capable of doing just that. A strong enough one hitting the earth directly would knock out any satellite facing the sun. So while it may not hit EVERY satellite, it would get more than half - remember the satellites are high above the earth.

So, if an alien race had large solar flare level technology, it would likely destroy a large portion of our satellites. Give that the majority of our space communications are over the northern hemisphere (most 1st world counties and land mass are there), this would basically destroy most of them if positioned appropriately.

See for instance:
https://sciencing.com/solar-flares-affect-communication-23537.html