The Spanish forward twisted his ankle in Sunday's derby defeat to Cardiff.
Swansea boss Michael Laudrup expects Michu to miss the Europa League clash with Kuban Krasnodar and the Premier League game against Stoke.
"Michu is not 100 per cent right now," Laudrup told reporters. "He is struggling with some physical problems and, on top of that, he had to leave the pitch with another twisted ankle so probably he will be out for a couple of games.
"It's hard to say (when he will be back) but if we are lucky then, because we have the international break, I hope he will be back for Fulham."