The Spaniard underwent a scan on his injured ankle after missing Sunday's 2-1 home defeat by Everton. The 27-year-old, who has scored six goals in all competitions this season, has had ankle and knee problems in recent months.
"It's not good news," manager Michael Laudrup told the club website (www.swanseacity.net) on Tuesday. "Unfortunately it has been confirmed that he will need an operation.
"The good news is that it can be done in the next week - and he should be back playing in around a month and a half.
"But what has happened in the last couple of weeks has changed things. We will probably do something now - in January - and try to add something that we don't have in certain positions," said Laudrup.
"The numbers are a bit down and that is risky for the last four months of the season."
Laudrup said he could sign Spanish forward Iago Aspas, 26, on loan from Liverpool.
"He is an interesting player but he is at Liverpool and they have injuries as well so that might not be possible," he added. "We are looking at other options."
Swansea, 11th in the Premier League, face Chelsea at Stamford Bridge on Thursday. They then travel to Aston Villa on Saturday before hosting free-scoring Manchester City on Jan. 1.
The club have received a boost after Welsh defender Ben Davies, 20, signed a new contract until 2017.
Laudrup said: "He's a very positive story. Not just for us but for Welsh football in general because it must be nice to see one of your own coming through.
"He came in and took his chance and the rest is history. He is doing well, playing for the national team and is still young."