Herbert, 24, is expected to be fully cleared for participation in offseason activities this spring.
It's unclear when Herbert suffered the injury. The Chargers were eliminated from the playoffs two weeks ago when the Jacksonville Jaguars mounted the third-largest comeback in NFL playoff history in the wild-card round.
Herbert played several weeks this season with fractured rib cartilage that he suffered in Week 2 but still threw for 4,739 yards and 25 touchdowns as the Chargers earned their first playoff berth since 2018.
Hebert was selected as an alternate for the AFC in the 2023 NFL Pro Bowl Games but will be unable to participate due to the surgery.