General manager Billy Eppler says Soto felt something in his right knee during Tuesday's game and that it locked up on him Wednesday. An MRI showed the tear.
Soto will have surgery and is expected to be out four to six weeks. He was hitting .298 with three doubles, three home runs and seven RBIs over the past 17 games.
"It's part of the game," Eppler said of the injuries. "You just fight through it."
The Angels recalled catcher Jett Bandy from Triple-A Salt Lake. He was expected to arrive during their game against the Dodgers. He will be the 36th player used by the team this season. He has hit .274 with 21 RBIs in 24 games with the Bees.
"He's been playing very well and catching very well," said manager Mike Scioscia, who coached Bandy when he was on the same Little League winter team with Scioscia's son Matt in the Los Angeles area.
The Angels have four pitchers and six position players on the DL.