The Spanish striker picked up an ankle injury in Sunday's 1-0 defeat to rivals Cardiff and will miss Thursday's Europa League meeting with Kuban Krasnodar and Sunday's Premier League clash with Stoke.
Laudrup was initially hopeful he would be available after the November international break, but speaking in Russia ahead of Thursday's match, he said: "Michu, our top scorer last season, has been struggling for a few weeks and is not 100 per cent and unfortunately he is out again for maybe three to four weeks."
Laudrup said the player, who has started every Premier League and Europa League game this term, has been affected by a problem with both his knees in recent weeks and has travelled to Spain for treatment.
"When I say he has not been at his best, it is because he has been struggling with both his knees for many weeks, but he wanted to play anyway and he is one of our most important players," said Laudrup.
"So with this ankle injury hopefully he can get both his knees sorted as well.
"He will be away in Spain for a few days for some injections."
Laudrup added: "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."