The 35-year-old Fowler sustained the injury while sprinting into second base on an attempted forceout during Friday's game against the Toronto Blue Jays. He beat the throw from Blue Jays shortstop Bo Bichette but didn't slide, causing him to arrive at the base awkwardly.
Fowler, who is scheduled to become a free agent after the season, immediately collapsed to the ground in pain.
The Angels initially diagnosed Fowler with a sprained knee, but a follow-up MRI revealed further damage. In a statement, the team said Fowler is expected to require six to nine months of recovery time after surgery.
"Comeback season has commenced," said Fowler, who doesn't believe the injury is career-ending. "The cards I've been dealt, so you've got to deal with them and go at it like that.
"... I want to continue to play. I think I've still got a lot left in the tank. Right now, I just want to get the knee back right and get going again."
Angels manager Joe Maddon said he plans to use Juan Lagares and Jose Rojas to replace Fowler.
Fowler, who was acquired from the St. Louis Cardinals in early February, was batting .250 with one RBI and a stolen base over seven games this season.