The team hadn't confirmed that diagnosis by the end of Wednesday's 7-5 loss to the Chicago Cubs.
The 31-year-old right-hander said he would continue to try to strengthen his arm but admitted surgery could be a possibility. Escobar, 18-7 with a 3.40 ERA last season, hasn't pitched this spring.
Angels manager Mike Scioscia said he's holding out hope that Escobar will pitch this season. But it seems certain he won't do so for quite some time.
"There's no certainty where Kelvim's going to be a month from now, that's for sure," Scioscia said. "But we're still optimistic that we're going to see him at some point. We still feel our pitching is a strength. If we start losing a couple of more guys, some of our answers might have to come from outside the organization, but we're not to that point yet."
The Angels will also be without 19-game winner John Lackey to start the season. The 29-year-old right-hander has a strained right triceps.
In addition to his 19 wins last year, Lackey led the AL with a 3.01 ERA.