23-year-old Taylor, who represented Team GB at this summer's Olympic Games, has undergone surgery after multiple fractures to his left ankle.
The break happened when his foot got trapped in the ground as he fell over, taking the full weight of Black Cats midfielder Craig Gardner on it in the process.
Swansea's head physiotherapist Kate Rees expects Taylor to make a full recovery, but says he will miss the rest of the season.
"The surgeons worked hard on Neil's injury... and did a very good job," she said to the BBC. "He is comfortable and the surgeons are happy with the operations.
"While he should make a full recovery, the extent of the injury means Neil is likely to miss the rest of the season.''
Taylor has become a key player for the Swans since signing for a tribunal £150,000 from fellow Welsh side Wrexham in 2010.
He has since gone on to become a regular starter in the Premier League and for the Welsh national team.
And Swans boss Michael Laudrup admits the incident was very unlucky and that no blame should be attached to Gardner for the unfortunate nature of the foul.
"When you have injuries like that it is normally very violent, but this was not violent," the Danish manager said. "It was even a free-kick against us.
"Sometimes these injuries happen in strange ways, you don't think anything is wrong and then there is ligament damage or something like that, it is very sad.
"But you see things that are much more violent than that - this was not violent, it was unlucky.
"He was very unlucky to fall in a bad way, you can't blame the Sunderland player for that."