Johnson, 29, was scratched from his scheduled start against the New York Yankees last week after feeling tightness in the triceps. The right-hander underwent an MRI that revealed no structural damage.
To replace Johnson on the active roster, Toronto recalled reliever Brad Lincoln from Triple-A Buffalo.
The Blue Jays also announced Thursday that Ricky Romero will be promoted from the minors and take Johnson's spot in the starting rotation. Romero, who was demoted to Single-A Dunedin after a lackluster spring training, will make his season debut Friday against the Seattle Mariners.
Acquired this past offseason as part of a blockbuster trade with the Miami Marlins, Johnson has struggled over his first four starts with the Blue Jays, going 0-1 with a 6.86 ERA.
Romero was Toronto's Opening Day starter in 2012 and had been projected as the fifth starter in the Blue Jays' revamped rotation this season. But after going 9-14 with a 5.77 ERA last season, the left-hander was demoted to the minors on March 26 after posting a 6.23 ERA in five spring starts.
Information from The Associated Press was used in this report.