The Blue Jays said in a statement Tuesday that Dr. James Andrews performed the operation. Johnson is expected to be ready for spring training.
The 29-year-old Johnson was acquired in a blockbuster deal with Miami last winter but was just 2-8 with a 6.20 ERA 16 appearances this year. He missed significant time with a triceps injury.
The club has yet to confirm whether it intends to extend Johnson a qualifying offer. He made $13.75 million this season.
Johnson made his big league debut with the Marlins in 2005 and has a career record of 58-45 with a 3.40 ERA.