
The Colombian defender, 31, damaged a ligament in his right knee in the second half of a round of 16 game Inter lost 2-0 at Anfield.
Cordoba is a mainstay central defender who joined the Italian champions in 1999. His club did not set a date for the surgery, but the player is likely to miss the return match with Liverpool on March 11, when Inter will be without his defence team-mate Marco Materazzi, who was dismissed in Liverpool.
Brazilian star striker Ronaldo, meanwhile, is set Friday to leave the Paris hospital where he was operated on last week for an injury similar to Cordoba's.
The ANSA newsagency reported that Ronaldo, 31, will continue the rehabilitation of his left knee in Paris until the end of February. His club AC Milan expect him back on the pitch by the end of the year.