Taylor sustained the injury during Saturday’s 2-2 draw against Sunderland.
The defender dislocated an broke his ankle in three places.
“The surgeons worked hard on Neil’s injury last night and did a very good job,” Swansea’s head physio Kate Rees told the club’s official website.
“He is comfortable and the surgeons are happy with the operation.
“While he should make a full recovery, the extent of the injury means Neil is likely to miss the rest of the season.”
