Yes, A Mars Quake Is A Thing. JPL Records A ‘Monster’ Temblor On The Red Planet

Southern Californians know all too well that the Earth is constantly moving and shaking, but it’s not the only place in the solar system that gets quakes.
Scientists at Jet Propulsion Laboratory in Pasadena picked up “monster” seismic movement on Mars last week through NASA’s InSight Mars lander.
The lander has had its mechanical “ear” to the Martian ground since it touched down in 2018, and it’s picked up thousands of tiny tremors. This quake was a magnitude 5, the largest ever detected on another planet.
“This is just as big as we had hoped for,” said Bruce Banerdt, the lead scientist on the InSight mission.
He said each “Mars quake” yields valuable clues about what’s going on inside the planet and how it formed billions of years ago.
“As the seismic waves move through the planet, they're reflected off of boundaries, like light reflected off a mirror,” Banerdt said. “So every time we have a quake, it’s like a little flashbulb going off.”
The record-setting quake may be the last big discovery for the lander.
Recent dust storms caked its solar panels with debris, forcing it to go into low energy mode, so it will only be able to transmit data for a few more months before the mission goes dark.

Obviously, Earth and Mars are very different places, and InSight’s seismological findings drive that point home. For starters, scientists are fairly certain that Mars doesn’t have the same kind of tectonic plates like here on Earth.
“We don't see large-scale transform faults, like the San Andreas fault [on Mars],” Banerdt said.
Instead, most seismic activity on Mars comes from what’s called “vertical tectonics,” like uplift from underground volcanic activity and other stresses coming from its interior.
Still, Banerdt notes there’s a lot of shaking going on.
“We think the level of seismic activity is pretty much what you might see on the Earth,” he said. “If you took away all the plate boundaries and the quakes associated with plate boundaries, and then you put that onto a smaller planet.”