Napoli was expected to remain at Massachusetts General Hospital for several days after the operation on Tuesday to improve the flow of air through his airway.
Sleep apnea sufferers experience shallow breathing or pauses in breathing during sleep that can last up to several minutes.
Napoli's performance declined from his strong 2013 season when he hit .259 with 23 homers and 92 RBIs to help Boston win the World Series. In 2014, he batted .248 with 17 homers and 55 RBIs. He also was bothered last season by a dislocated left ring finger that didn't require surgery.