The Dutch midfielder lasted just nine minutes against Sheffield United on Saturday in his first start since recovering from cruciate damage that kept him out since last November.
Bodde was sent for a scan on Sunday and was given the news he did not want to hear on Monday.
Swansea physio Cerian Parham told the club's official website: "The replacement graft has ruptured. It's very rare for this to happen as the graft is normally stronger than the original ligament."
The 27-year-old suffered the original injury against Birmingham last year and had been gradually eased back into action by boss Paulo Sousa.
Bodde has proved to be a key player for the Swans since his move from ADO Den Haag two years ago and was the subject of transfer bids from Wigan and Bolton this summer.