The defender will undergo shoulder surgery on Wednesday, having consulted with a specialist on Monday.
The Welshman was carried off after just 13 minutes of the Hoops' 2-0 win over Motherwell at Celtic Park on Saturday.
The lengthy lay-off means he will play no further part in the Champions League group stages.
A statement on Celtic's website confirmed: "Adam Matthews saw a specialist today and he will undergo shoulder surgery on Wednesday.
"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."