Matthews suffered the blow during the Scottish champions' 2-0 win over Motherwell at Celtic Park on Saturday.
Celtic have four matches remaining in Champions League Group H. They face Ajax on October 22 and November 6, AC Milan on November 26 and Barcelona on December 11, with Matthews unlikely to return until next year.
Celtic said in a statement: "Adam Matthews saw a specialist today (Monday), and he will undergo shoulder surgery on Wednesday. It is likely that he will be out for between 10-12 weeks.
"The Welshman was injured after just 13 minutes of the game at Celtic Park on Saturday against Motherwell, and was stretchered off, to be replaced by James Forrest.
"Everyone at Celtic sends their best wishes to Adam ahead of the surgery and for the weeks ahead."