Richards' knee buckled when he was covering first base during a game against the Boston Red Sox. He was treated on the field for 10 minutes before being carted off on a stretcher.
The expected recovery time from the surgery is six to nine months, which could extend into the start of the 2015 season.
The loss of Richards is a big blow for the first-place Angels in their bid to win the American League West title and reach the postseason.
Richards, having an ace-like season with a 13-4 record and a 2.61 ERA in 26 starts, went down in a heap covering first base in a game against the Boston Red Sox in Fenway Park and suffered what manager Mike Scioscia called at the time "a significant injury."
"It's a tough night," said Scioscia, whose team entered Thursday's play leading the Oakland Athletics by 1 1/2 games in the AL West with seven games between the teams coming up the next two weekends. "I can't tell you how bad we feel for Garrett and how hard he's worked. ... This is a tough night for us."
The 26-year-old Richards is the second member of the Angels' rotation to go down: Left-hander Tyler Skaggs underwent Tommy John elbow surgery earlier this season.
Scioscia made it clear that the show must go on and the Angels rallied from three runs down and routed the Red Sox 8-3 on Wednesday night -- with six relievers finishing the game after Richards left for Massachusetts General Hospital in the second inning.