He is expected to miss at least six months, The Athletic is reporting.
The left-hander had been the subject of trade rumors since he will be a free agent at the end of the 2019 season. He was set to earn over $12 million in arbitration.
Britton, 29, was the most dominant reliever in baseball in 2016. He led the league with 47 saves and had a 0.54 ERA and 0.836 WHIP. He was an All-Star and finished fourth in Cy Young voting.
But injuries slowed him last year. An MCL strain in his left knee required platelet-rich-plasma treatment.
He was limited to 38 games, had a 2.89 ERA, 1.527 WHIP and 15 saves.