In an issued statement, the Red Sox said following a Monday examination, doctors determined Bailey "should undergo surgery to reconstruct the ulnar collateral ligament in his right thumb."
"The surgery is scheduled to be performed by Dr. (Thomas) Graham tomorrow in Cleveland."
The Bosox acquired the right-hander from Oakland in late December, after which he signed a one-year deal to avoid arbitration.
The team didn't say how long Bailey would be sidelined, but the recovery time from such surgery is typically three months, ESPN reported.
The broadcaster said Bailey apparently hurt the thumb in a collision during a March 21 spring training game against Pittsburgh.
The 27-year-old racked up 24 saves in 42 games for the A's last season, going 0-4 with a 3.24 earned run average.