La Stella was removed in the sixth inning of Los Angeles' 9-4 win over the Rangers on Tuesday. He was helped off the field after being examined by the training staff and manager Brad Ausmus.
The injury comes after La Stella got named to the American League All-Star team for the first time in his career.
After being acquired by the Angels last November in a trade with the Chicago Cubs, La Stella has been a breakout star in 2019. The 30-year-old has more home runs in 78 games this season (16) than he did in 396 games from 2014 to 2018 combined (10).
La Stella also ranks second among Angels regulars with a .300 batting average and is tied for second with 44 RBI.
The Angels will likely turn to rookie Luis Rengifo as La Stella's replacement at second base. The 22-year-old is hitting .247/.321/.370 with three homers and 19 RBI in 47 games.