Scioscia added that Escobar first experienced tightness while legging out a single in the fifth, then felt it again while scoring from second base on Albert Pujols' game-tying, two-run single.
The infielder left the game, having gone 1-for-3 on the evening with two strikeouts, and was replaced at third by Cliff Pennington with the score even at 2-2.
Escobar, 34, has been the Angels' leadoff hitter in 37 games this season, and has been enjoying a recent hot streak. He entered Saturday's game with a .358 average (19-for-53) over his last 12 games, and his production at the plate leaves the Halos with a key hole to fill in the interim.
Scioscia said the team will evaluate its options at third, should Escobar miss any extended time.
"We have Cliff, we have Luis [Valbuena] and Jefry [Marte]," he said. "We'll match up one of the guys. Luis or Jefry have to play first base, then we can look at some stuff and see who will go to third and make those decisions."
Kaelen Jones is a reporter for MLB.com based in Los Angeles. This story was not subject to the approval of Major League Baseball or its clubs.