The defender was carried off on a stretcher after falling awkwardly in the closing stages of the 4-1 EFL Cup win over MK Dons on Tuesday.
Swansea 6/4 to be relegated
Scans have since revealed that the 26-year-old has damaged the medial ligament in his left knee and he will see a specialist next week for further assessment.
The Swans expect him to be out of action for between six and eight weeks while he recovers.
Bartley, who spent last season on loan at Leeds United, signed a new contract in August and has featured in all three of Swansea’s games so far in 2017-18.
Earlier on Thursday, the Premier League club confirmed the signing of defender Jack Bainbridge on a free transfer.
The 19-year-old, who joins on a one-year deal after leaving Everton, will play for the Under-23 side.
