The 27-year-old was withdrawn from the action midway through the second half at the Cardiff City Stadium.
Michu has scored 28 goals for Swansea since joining from Rayo Vallecano in July 2012, but he failed to make an impact as Steven Caulker's second-half header against his former club secured victory for Cardiff in the first top-flight meeting between the South Wales rivals.
And Swansea manager Michael Laudrup confirmed that Michu is set for a spell on the sidelines as the side face the likes of Kuban Krasnodar, Stoke City and Fulham in the next fortnight.
"Michu is not 100 per cent right now," Laudrup said.
"He is struggling with some physical problems and, on top of that, he had to leave pitch with another twisted ankle so probably he will be out for a couple of games."
Laudrup expressed his disappointment at losing to fierce rivals Cardiff, but insisted that Swansea had dominated the game.
"It ended up being disappointing," he added.
"It is always that way when you lose a derby and we really wanted to win.
"Our plan in the first half was to control it and we did that quite well, we kept them away from any chances.
"When we wanted to bring on some players to go for the game, they scored from a set-piece. We knew that they were strong from these and it's one of the only chances they had from the game."
Goalkeeper Michel Vorm was sent off in the closing stages for Swansea after bringing down Cardiff striker Fraizer Campbell, a decision that Laudrup refused to dispute.
"He was the last man, everything happens so quickly," Laudrup explained.
"From the outside, it seemed like he was the last man so it seems like it was ok. The referees need to take that decision in a split second so that's what can happen."
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