The 27-year-old, who has scored 28 goals for the Swans since joining from Rayo Vallecano in the summer of 2012, has been hindered by ankle and knee issues throughout the current campaign.
The Spain international's frustrations have been clear to see, and manager Michael Laudrup has confirmed the player will need to undergo a procedure on his right ankle.
"It's not good news," said the Dane. "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 loss of Michu further dents Swansea's attacking resources with winger Nathan Dyer likely to be sidelined until February after suffering an ankle ligament injury in the recent draw at Norwich.
Laudrup admits the combination of the two injuries means it is likely he will look to bring in a forward during the January transfer window.
Laudrup said: "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.
"The numbers are a bit down and that is risky for the last four months of the season."
Among the players Laudrup has been linked with a move for is Liverpool striker Iago Aspas, who he actively pursued last summer.