Deadline reports that the actor will appear in the fourth season finale and could also recur in the following season.
He will play Max, a "brilliant, plugged-in operator" who is an old friend of Michael (Jeffrey Donovan).
Baker recently appeared in episodes of Ugly Betty and The Good Wife and also played Dr. Curt Connors in the second and third Spider-Man films.
The Burn Notice summer finale aired on August 26. The fourth season will resume on November 11.