The full-back suffered the injury in last week's 5-1 Europa League play-off first-leg win over Romanian side Petrolul Ploiesti but he was able to train on Thursday and Friday.
However, the injury flared up again and Taylor was taken to hospital as a precaution.
Swansea head physio Kate Rees said: "Neil picked up a slight dead leg in the Europa League game last Thursday but he was able to train on Friday and Saturday.
"However, the haematoma re-bled on Sunday and he was admitted to hospital as a precaution.
"While there is no serious muscle or tissue damage, he suffered severe swelling and bruising to his thigh which will take between four to six weeks to clear up."
It means the left-back will now miss the return tie in Romania and is likely to miss out in Premier League games against West Brom, Liverpool and Crystal Palace, as well as Wales' next two World Cup qualifiers against Macedonia and Serbia.
Nathan Dyer will also miss the tie in Romania on Thursday as he continues to struggle with a hamstring injury.