Voyager: If you are on a ship, can you feel an earthquake/tsunami?

Depending on the location of a ship, people onboard can feel both earthquakes and tsunamis.
 
The rapid vertical movement of the seafloor, which abruptly displaces a large volume of seawater, causes tsunamis. This displacement can be from fault movements, as occurred recently off Chile, or from the rapid downward slide of a slope.
 
For example, a strip of seafloor uplifts and sends a tsunami wave in two directions, toward the nearby coast and toward the open sea.  As the tsunami approaches the coast, it begins to break in shallow waters and can crest with a height of several meters. Any ship in harbor or near the coast will certainly feel the wave and may be pushed inland.
  
In the other direction, the wave travels into the deep ocean at the speed of a jet airliner. The entire wave can be 100 kilometers (62 miles) long and take up to an hour to pass a ship. However, its height is usually less than a meter (3.3 feet) and because it takes so long to pass a ship, it’s usually not felt by anybody onboard. As the wave crosses the ocean and nears a distant coast, it slows and “piles up,” or crests, and again would be felt by a ship near the coast.
 
Seismic waves from an earthquake can emerge from the seafloor as an acoustic (sound) wave that travels through the ocean toward the surface and can strike a ship. If the sound is strong enough, the ship will be violently rocked. These are called seaquakes. Seaquakes can be so strong that sometimes those onboard think they have hit ground.  

— Dave Chadwell, associate research geophysicist, Marine Physical Laboratory