The Spaniard was sent for a scan on Monday, which confirmed the need for an operation on his right ankle.
"It's not good news," Laudrup told the press. "Unfortunately it has been confirmed that he will need an operation.
"It can be done in the next week and he should be back playing in around a month-and-a-half."
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The absence of the 27-year-old is a major blow for the Welsh club and Laudrup has revealed that he plans to enter the transfer market next month to bolster his forward line.
Liverpool striker Iago Aspas has been linked with a loan move to the Liberty Stadium and the Dane confirmed his interest in the former Celta Vigo man but is not optimistic that Liverpool manager Brendan Rodgers would allow Aspas to leave Merseyside.
"What has happened in the last couple of weeks has changed things," the Swans boss conceded. "We will probably do something now [in January] and try to add something that we don't have in certain positions.
"The numbers are a bit down and that is risky for the last four months of the season. [Aspas] is an interesting player but he is at Liverpool. They have injuries as well, so that might not be possible but we are looking at other options.
"A lot of clubs will do business and everyone needs players in certain positions. We just have to do our best and not talk about names."