Trout, 29, exited Monday's game against the Cleveland Indians after being seen limping on the basepath.
"I've never felt anything like this before; I felt a pop," Trout said Tuesday, according to Alden Gonzalez of ESPN. He added that he was initially worried he had ruptured his Achilles.
"If you come back too soon, I could tear it again," the outfielder said, according to Mike DiGiovanna of the Los Angeles Times. "Have to be smart about it and hopefully heal soon."
L.A. placed the eight-time All-Star and three-time MVP on the injured list and later recalled left-handed pitcher Jose Quijada from Triple-A. Quijada, 25, made six appearances for the Angels last season, posting a 7.36 ERA and 5.92 FIP in 3 2/3 innings as a rookie.
Trout boasts a .333/.466/.624 slash line with eight homers and two stolen bases so far this season, leading the American League in both OBP and SLG.
The Angels currently sit fourth in the AL West at 18-22 and are a half-game up on the last-place Texas Rangers.