Matthews was stretchered off in the early stages of Celtic's 2-0 win over Motherwell at Celtic Park on Saturday and is due to undergo surgery on Wednesday.
"Adam Matthews saw a specialist today (Monday) and he will undergo shoulder surgery on Wednesday," read a statement on Celtic's official website.
"It's likely that he will be out for between 10-12 weeks. Everyone at Celtic sends their best wishes to Adam ahead of the surgery and for the weeks ahead."
Matthews has withdrawn from the Wales squad for their forthcoming FIFA World Cup™ qualifiers against Macedonia and Belgium.