2001 Civic auto Inner CV joint wobble

I have a 2001 Civic w/ auto trans and is has developed a heavy rhythmic vibration occasionally around 40 MPH. Lift off of the gas pedal and it goes away. Definitely on the driver’s side. Front end is tight, except there seems to be a lot of wobble in the inner CV joint where it goes into the trans-axle. The right side CV joint moves very little up and down when try to wiggle it. Have you seen this cause vibration?