The Angels placed Escobar on the 10-day DL Sunday after an MRI revealed a grade 1 strain of his left hamstring.
Escobar, 34, suffered the injury in Saturday's game against the Detroit Tigers. The 11-year veteran is batting .272 with five home runs and has scored 22 runs as the Angels' leadoff hitter this season.
"Escobar kind of sets the pace at the top of the order," Angels manager Mike Scioscia told reporters Sunday, according to MLB.com. "We're going to miss Yunel for as long as he's out."
Scioscia said the Angels likely will rotate players at third base while Escobar is sidelined. Luis Valbuena started at third base Sunday, and Jefry Marte and Cliff Pennington also can play the position.
"We'll definitely have enough depth to rotate some guys and get them off their feet," Scioscia said. "But we also need to establish some continuity."