Routledge, who has missed only three of Swansea's 22 league games this season, was injured during his side's 5-0 home defeat by Chelsea on Saturday.
Ecuadorian international midfielder Jefferson Montero is available again, however, after recovering from a hamstring injury sustained in the December win against Aston Villa.
Swansea are away to Championship (second tier) side Blackburn Rovers in the fourth round of the FA Cup on Saturday when they will also be without skipper Ashley Williams, who injured his shoulder against Chelsea.

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