Manager Matt Williams gave the new Thursday after Stammen had an MRI. The operation has not yet been scheduled.
''Depends on the extent of the damage,'' Williams said of Stammen's chance of missing the season.
The 31-year old right-hander appeared in five games - all in relief - without allowing a run in four innings. He went on the disabled list Wednesday.
''It's never good news,'' Williams said of the surgery. ''But knowing him, he'll rehab as quick as he can, as hard as he can, and be back at some point. We just don't know the time frame.''
Rivero, 23, will be making his major league debut.