Can massage therapy cure tendonitis of the shoulder?

Sometimes: You need to get a really well trained therapist with a lot of experience and start slow.

No: To an extent the answer depends on which tendon is involved. Massage can aid in the recovery of injured tissue by stimulating blood supply, and in the case of a tendon mobilizing it. In general tendons do not repair if their is much tearing, but in the case of minor tears seen in inflammation (tendonitis) improve with gradual strengthening and judicial use of steroids for pain management.