Bradley, 28, revealed the injury to Phillies brass after giving up a run on two hits in Saturday's loss to the Atlanta Braves.
"It's not something I can pinpoint," Bradley said on Sunday afternoon. "It wasn't one particular act that I felt it on."
Bradley was a major offseason addition to the Phillies' bullpen, which had a historically bad season in 2020. He gave up runs in two of his four appearances this year before heading to the injured list.
This is Bradley's first experience with an oblique ailment, which can take considerable time to heal, depending on the severity. The righty wasn't sure on a timetable for his return.
"It's not something I felt doing baseball activities," Bradley said. "Honestly, I don't know where it came from."
The Phillies recalled lefty JoJo Romero from the alternate site to take Bradley's place on the roster. Romero was a late cut from spring training but is now needed just over a week into the season.
"He's throwing the ball pretty well," manager Joe Girardi said of Romero.