Reddick is scheduled for three weeks of rest before beginning a month-long rehab program and is expected to be ready for spring training.
"It's all good," the source said.
Reddick, 24, played a total of 87 games for the Red Sox in 2011 and posted a .280 batting average with seven homers and 28 RBIs. With J.D. Drew's career in Boston over, Reddick will have a legitimate chance to compete for the starting job in 2012.
Reddick, who has dealt with a wrist issue in the past, was also drilled in the left hand by a pitch during a game on Sept. 4 against the Texas Rangers where he went 4-for-4 with a double, scored three runs and reached base for a career-high five times to help Boston to a 12-7 victory that day.
Reddick was a late addition to the team of major league players that toured Taiwan earlier this month for a series of five exhibitions. He served in a backup role and played in the next-to-last game of the series without any evidence that his wrist was bothering him, but before the final game he had the wrist wrapped and kept the wrap on for the long flight back home to the U.S.
Joe McDonald covers the Red Sox for ESPNBoston.com. Information from ESPNBoston.com's Gordon Edes was used in this report.