The forward was forced from the field by the issue in the second half of Sunday's 1-0 South Wales derby defeat at Cardiff City, and was initially expected to miss just a couple of fixtures.
However, manager Michael Laudrup has revealed the Liberty Stadium club's star man was already suffering from pain in both knees, and hopes a trip to Michu's homeland will aid his recuperation.
"Michu has been struggling and now he is out again for maybe three or four weeks," said Laudrup.
"At times he has not been at his best because he has been struggling with both his knees for a few weeks.
"Now he has injured his ankle as well. He will go away (to Spain) for a few days and hopefully everything will get better at the same time."
"Three to four weeks was the first medical opinion. But we said Ben Davies would be out for three to four weeks and he is back training with us now (after two weeks).
"It is always better to do it that way, to say a little more rather than reduce it and say it is three weeks and it ends up being five."
Michu has scored six goals in all competitions for Swansea this season.
Laudrup's men head to Russia on Thursday to face Kuban Krasnodar in the UEFA Europa League, knowing a win could send them into the next round.
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