The 27-year-old Spaniard has scored 28 goals for the Swans since his bargain move from Rayo Vallecano, but was hurt in Sunday's derby defeat against Cardiff.
Laudrup had said at the time that Michu would definitely miss Thursday's Europa League clash with Kuban Krasnodar and Sunday's Premier League meeting with Stoke, but was hopeful he would be available again after the international break.
However, at his pre-match conference in Russia, Laudrup suggested the Spain international may be out for longer at a time when he is desperately needed, with Swansea lacking a clinical edge in front of goal.
"There are some players not at their best," said Laudrup.
"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."
Such a diagnosis would mean Michu, who has started every Premier League and Europa League fixture so far this term, will not potentially return until the December 4 meeting with Newcastle.
Laudrup was keen to make clear that is a worst-case scenario, but also revealed the player has been affected by a problem with both his knees in recent weeks and has gone to Spain for treatment on his various ailments.
"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."
Swansea (from): Vorm, Amat, Taylor, Flores, Williams, Britton, Shelvey, Bony, Dyer, Lamah, Routledge, Tiendalli, De Guzman, Canas, Rangel, Pozuelo, Tremmel, Vazquez.