Depends largely on what you want to do.
If you want to be working as an industrial designer, you need an industrial design portfolio and corresponding skills. An addition degree is the typical way to build this portfolio for someone in your position.
If you want to be a mechanical engineer working within product development or industrial design – it’s more about your engineering career path and current experiences. You can work heavily with designers, and may have some light design input. Grad school for this is less likely but not impossible (Stanford, CMU both come to mind as having strong PD programs that help situate engineers within design fields).