According to this source, in the open ocean, a tsunami in the open ocean is typically less than 1 meter high. Some of the more more sensitive radar surveillance satellites have a resolution of 4-5 cm and should be able to detect that kind of wave. However, they're in LEO, meaning their coverage over a given area is limited to a few minutes. There aren't very many of these satellites, so the revisit time can be several hours before you can image an area again. As an example, TOPEX/Poseidon has a repeat period of 10 days. To get wider area coverage, you need higher orbits but that makes it harder to get the resolution. You'd need bigger and more powerful radars and have to handle much more data. As for optical detection, a LIDAR could give you good resolution but then there's problems in cloudy areas.

Perhaps if the satellites could be cued to look at specific areas based on seismic readings from the ground, we might be able to detect an open water tsunami from space. We'd need to get more radar altimeters on satellites to increase the coverage and shorten revisit intervals. You'd need to compare the data with existing data to separate the measurements from ocean topology. It's pretty complicated.