The latest procedure is set for Friday. Martinook is expected to miss six to eight weeks to recover.
He also underwent a procedure on a core muscle during the offseason.
Martinook, 26, has one assist this season during the Hurricanes' 4-0-0 start. He had a career-best 15 goals with five game winners last season but was in and out of the lineup during the playoffs due to injuries.
Information from The Associated Press was used in this report.