The 35-year-old was stretchered off in the early stages of Saturday's goalless draw with Nottingham Forest and the Lions today confirmed the severity of the injury.
Millwall physio Bobby Bacic told the club website: "Carlos has had a scan earlier today and, as feared, it has shown that he has significant knee ligament disruption involving the cruciate and lateral ligaments. He has also sustained a rupture to the hamstring muscle.
"Carlos will be seeing a specialist tomorrow with a view to surgery."
Edwards, who joined Millwall permanently this summer after a loan move from Ipswich Town last season, had played every minute of the 2014-15 season before his injury.