The Angels also designated second baseman Johnny Giavotella for assignment and reinstated first baseman C.J. Cron from the disabled list. Cron had surgery to repair a bone in his left hand on July 14.
Escobar was hurt in the fourth inning of Friday night's 7-0 loss to the Yankees and left the game. Manager Mike Scioscia later said Escobar was hit in the nose and cheek.
Escobar is batting .320 with three home runs and 34 RBIs in his first season with the Angels.
Cowart was hitting .280 with nine homers and 58 RBIs for Salt Lake. In three games in the major leagues this season, he went 1-for-6.