Janssen, 34, was informed he wasn't going to make the Opening Day roster and he requested to be released.
"He was getting further and further behind the 8-ball," Padres manager Andy Green told reporters. "Out of respect to someone like himself, who has done so much in the game and been so successful, rather than hold him until his last day of his out clause, we allowed him his release today."
Janssen, who was a nonroster invitee, allowed four runs on 12 hits over seven spring innings.
Janssen was 2-5 with a 4.98 ERA in 48 games for the Washington Nationals last season.
He spent eight seasons with the Toronto Blue Jays and recorded a career-best 34 saves in 2013.