Routledge, who has featured in 19 of the club's 22 Barclays Premier League fixtures this campaign and scored three times, came off after only 32 minutes of last weekend's 5-0 home defeat to Chelsea.
But there was better news for Swansea manager Garry Monk on Tuesday as Ecuador international Jefferson Montero returned to full training for the first time since sustaining a hamstring injury in the 1-0 victory against Aston Villa on Boxing Day.
Montero will be available for selection for Saturday's FA Cup fourth-round trip to Sky Bet Championship side Blackburn and midfielder Leon Britton is also in contention for that game after missing the Chelsea defeat with a groin strain.
But captain Ashley Williams is set to miss the trip to Ewood Park after sustaining a shoulder injury against the Premier League leaders.