Lucky for us, the end won't be exactly like in the movies. It’ll still be insanely awful, mind you. Just a different kind of awful. Scientists have created simulations to get an idea of exactly how a colossal space rock impact would go down, and it turns out that gigantic ocean waves will be the least of our problems as they actually tend to teeter out and vanish pretty quickly. It’s kind of like when you throw a rock into a pond — the immediate ripples are big, but they become smaller the further out they go.
Tsunamis are almost always caused by earthquakes. That is, activity happening on the ocean bottom that causes a displacement of water as the pressure spreads out and up. Space rocks come from above, so it’d make sense that, yes, they’d cause a great big splash — any nearby ship would surely be wrecked — but they probably won’t create a tsunami. In fact, a big rock falling from space into our ocean will be terrible at making waves because it'll lose 80% of its impact energy to the huge amount of water that’ll immediately vaporize.