The Spanish forward picked up the injury in the second half of his side's 1-0 loss and was replaced by Wilfried Bony.
Manager Michael Laudrup expects the 27-year-old to sit out fixtures against Kuban Krasnodar in the Europa League and Stoke in the Premier League, but hopes extra recovery time over the international break will see him back to face Fulham on 23 November.
"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."