Burnett, who has been on the disabled list since May 28, said Wednesday that a "little tear" was found during an MRI exam by the Texas Rangers' team physician, Dr. Keith Meister.
"He's definitely not going to pitch this year," Angels manager Mike Scioscia said. "This is huge. You look at what Sean could do, and Ryan Madson (who has missed the entire season). Losing them has stretched out the roles and diluted the bullpen effectiveness."
Madson has been on the disabled list all season while recovering from Tommy John surgery that forced him to miss all of last season with Cincinnati.
Burnett was on the DL for three weeks earlier this season because of left forearm irritation, and was back for only a week before going back on the DL with the elbow problem. In 13 games for the Angels this season, he allowed one run in 9 2-3 innings.
Burnett had the MRI after experiencing "a little discomfort" when throwing off a mound Monday.
The left-hander said he was deciding whether to have surgery and would talk next week with Dr. James Andrews, who performed ligament replacement surgery on Burnett in 2004 when he was with the Pittsburgh Pirates. Burnett missed all of 2005, but said surgery for this injury would be a simpler procedure, and that he should be ready for spring training.
Burnett, who signed a two-year deal with the Angels last winter after 3½ seasons with Washington, said the doctors had told him his recovery period would last no more than 5 months.
Angels relievers went into Wednesday night's game ranked 13th in the American League with a 4.21 earned run average.