The right-hander, signed in November to an $8 million, one-year contract, was placed on the disabled list before the season began. He strained his elbow during spring training, and the Padres initially thought he would be out about one month.
Johnson had surgery on his right elbow in the offseason to remove bone spurs. He was examined after the latest setback by Dr. James Andrews, who performed Tommy John surgery on Johnson in 2007.
The 30-year-old Johnson was a two-time All-Star with the Marlins. He was 2-8 with a 6.20 ERA last season with Toronto.
"This is a tough one. You know Josh Johnson has been banged up the last couple of years. He was really, really hopeful for this season," Padres manager Bud Black said before the team's game Wednesday night at Milwaukee.
San Diego thought Johnson was over his problems following his offseason surgery. Black said Johnson will work hard to return to the mound.
"Any time you go in for a second Tommy John surgery, it raises some eyebrows," Black said. "If anyone can come back, it is Josh Johnson."