The news is a major blow for a club 18th in the league, two points behind 17th-placed Southampton, and battling to avoid relegation after three successive defeats.
"Unfortunately, our biggest fears have been confirmed regarding the injury Sol suffered at Wolves on Saturday," manager Neil Warnock told the club website (http://www.cardiffcityfc.co.uk).
"Scans have shown that Sol has ruptured his ACL; he will have an operation on Wednesday and therefore miss the rest of the season."
Bamba was carried off the pitch on a stretcher during the first half of the 2-0 defeat at Wolverhampton Wanderers on Saturday.
The 34-year-old Ivory Coast international has scored four goals this season and played in all but one of Cardiff's 29 league games.
(Reporting by Alan Baldwin, editing by Ed Osmond)
