Since motion sickness is a complex syndrome based on the confusion of various inputs to the brain, and since plants don’t have brains, the answer is NO.

@elbanditoroso Is shock a better term? I know that some house plants can die from moving them.

Shock is not a “better” term, it describes something different.

Motion sickness is from a disruption in the vestibular system. Since plants don’t have such organs, as @elbanditoroso said, the answer is “nope.”

If plants were subject to motion sickness, we would see evidence of it whenever the wind blows.