Richards, who was placed on the 60-day disabled list, is scheduled to undergo surgery next week. He sustained the injury Wednesday night against the Red Sox while covering first base in the second inning.
First baseman Albert Pujols had fielded a ground ball by Brock Holt and thrown to second for a force play with Boston runners on first and second. Richards never made it to the bag, as he fell to the ground, clutching his left knee in pain.
General manager Jerry Dipoto said Thursday "we'll be open" about finding a deal to replace Richards in the rotation. The Angels selected the contract of left-hander Wade LeBlanc, who pitched briefly for the New York Yankees earlier this season, from Triple-A Salt Lake.
Richards, who was taken off the field on a stretcher, flew back to Los Angeles on Thursday to be examined by team doctors.
"Obviously he's very distraught," Angels manager Mike Scioscia said after the Angels' 8-3 win. "He knows that it's not good."
Richards took a 13-4 record and a 2.53 ERA into Wednesday's game in what has been a breakout season for the 26-year-old right-hander. He entered the game having struck out 100 batters in 100 1/3 innings since June 4 while posting a 1.79 ERA. Richards was tied with Felix Hernandez for the American League lead in batting average against.
This is another blow to the Angels' rotation. Tyler Skaggs has already been lost to Tommy John surgery that will sideline him until the start of the 2016 season.
On Monday, the Angels took over sole possession of first place in the AL West for the first time since May 15, 2011.
Information from The Associated Press was used in this report.