A tsunami can be generated by ANY disturbance that displaces a large water mass from its equilibrium position. There are two categories for the trigger mechanism of a tsunami:
Terrestrial trigger mechanism are most often earthquakes, however, undersea landslides, volcanic eruptions, and explosions can also cause a tsunami.
Extraterrestrial trigger mechanism are impacts of cosmic bodies, such as meteorites in the ocean. Of course, these are rare occurences but is theorized that the disappearance of the dinosaurs can be linked to impacts of extraterrestrial material in the ocean which caused various large tsunami and destroyed everything in it's path.
In the case of earthquake generated tsunamis, the water is disturbed by the movement of the sea floor.