The central defender is expected to play again this season having discovered he has ruptured a medial ligament and not damaged the same cruciate ligament that saw his miss almost the entire 2006/07 campaign.
Monk sustained the injury just minutes after scoring City`s opener in Saturday`s 4-0 FA Cup victory over Colchester.
He is yet to discover whether he will need surgery, but Swansea head physio Kate Rees told the club`s official website: "It`s a lot better than we expected. Our initial fear was that his cruciate ligament had gone again.
"That would have ruled him out for the rest of the season and up to nine months. But there is no damage to his old injury and the worst scenario is a three-month rehabilitation process.
"But Garry is a player who has always worked hard on his rehab in the past and if anyone can get back quicker then it will be him."