IIRC most ideas for FTL travel don't involve traveling through normal space, so particulate matter wouldn't be an issue.
In Star Trek style FTL (as envisioned by the Alcubierre Drive), the ship stays within a small bubble of normal spacetime. It's not moving at all by any normal metric. However, the bubble itself is moving at incredible speed. This gets around relativity because you're not actually going faster than the speed of light in normal space. You're just bending normal space around you and riding through that bubble. A more realistic comparison would be a supercavitating torpedo. Due to the bubble of air around it, it's able to move through the water much faster than if it had to push through all that water on its own.
The caveat to the Alcubierre Drive (although not proven, and they don't know how to get around it if it IS a thing) is that you would generate large amounts of gamma radiation on the leading edge of that bubble. And when you drop back into normal space, all that radiation would get blasted forward, which would cause a very, very bad day for any planet in front of you.
So tl;dr - you wouldn't have to worry about impacts, just turning your destination into an irradiated wasteland.