Although a postgame X-ray returned negative, Simmons later underwent an MRI that confirmed the injury. He'll visit a foot and ankle specialist on Wednesday.
The Angels did not provide any additional information on the injury but a Grade 3 sprain is generally considered to be the most serious classification. Simmons was using crutches when he met with the media Tuesday and was unable to offer a timeline for his recovery, according to J.P. Hoornstra of the Southern California News Group.
Simmons jammed his ankle while crossing first base as he tried to beat out a grounder in the eighth inning of Monday's game, and he needed to be helped off the field.
The four-time Gold Glover missed 11 games last season due to a sprained right ankle. However, it was classified as a less severe Grade 2 sprain, according to Fabian Ardaya of The Athletic.
Simmons has been a rock for the fourth-place Angels this season. In 46 games, the 29-year-old is slashing .298/.323/.415 with three homers, 21 RBIs, and five steals, while playing his usual otherworldly defense at shortstop (four defensive runs saved, 3.6 ultimate zone rating).
Infielder Luis Rengifo was recalled from Triple-A Salt Lake to take Simmons' roster spot. Rengifo, who's appeared in 11 games for L.A. this season, will hit eighth and play second base on Tuesday against Minnesota, while David Fletcher will man shortstop in place of Simmons.
Despite losing Simmons, the Angels did receive one piece of good injury news on Tuesday. Designated hitter Shohei Ohtani, who sustained a finger injury when he was hit by a pitch moments after Simmons was hurt, is healthy and in the lineup for Tuesday's game.