Michu, 27, has scored 28 goals for the Swans since signing from Rayo Vallecano in the close season in 2012 but has been hampered all this season by ankle and knee problems.
"It's not good news," said Laudrup. "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."
The news is a further blow for Swansea after losing winger Nathan Dyer until February after he suffered an ankle ligament injury against Norwich.