Richards will undergo surgery, which the Angels said would take place next week. He is expected to be sidelined six to nine months.
Richards, 26, crumpled to the infield Wednesday night after he pulled up while covering first base on a ground ball in the second inning of a game against the Red Sox.
He spent eight minutes on his back, writhing in pain as medical personnel attended to him and Angels first baseman Albert Pujols tried to comfort him.
Richards began the game with a 13-4 record and a 2.53 earned-run average. The young right-hander had become the Angels' ace, holding opponents to a .195 batting average and accumulating 164 strikeouts in 167 innings.
He was getting even stronger as the season wore on, with a 1.79 ERA and 100 strikouts in 14 starts since June 4.
The Angels entered the final game of their series against the Red Sox on Thursday with a record of 75-50, the best in baseball, good for a 1 1/2-game lead over the Oakland Athletics in the American League West.
"It stinks," Angels catcher Chris Iannetta said when he heard the final diagnosis. "We know Garrett is the one suffering the most. We know how badly he wants to be in the race and finish the season with us.
"We're all hoping he recovers and has a long and healthy career. He needs to focus on his recovery. We need to focus on this playoff race."
With runners on first and second and one out in the second inning Wednesday, Richards induced Brock Holt to hit a ground ball to Pujols, who fired a strike to second base for a forced out. Richards had sprinted from the mound to cover first, hoping to receive a throw from shortstop Erick Aybar for a potential double play. But as he approached the bag, he caught his right cleat in the dirt and his left knee buckled.
Several Angels players and Manager Mike Scioscia visited Richards at the team hotel Wednesday night, offering encouragement.
"We're going to be thinking of Garrett every fifth day," Scioscia said. "We might not be able to replace him but that doesn't mean that we're not going to be able to reach our goal as a cumulative pitching staff."