The Ivory Coast international strained his hamstring in the Europa League clash at the Liberty Stadium, and will now undergo scans.
"It could be quite a serious one. We'll have to wait two or three days until we get a scan but unfortunately we are talking several weeks," Sky Sports News quotes Laudrup as saying.
"It is a blow but that's how it is. You have to accept it and when you have a lot of games this is a possibility.
"Let's see what happens with Michu in the next week or so."
Dani Parejo scored the deciding goal for Valencia in the 20th minute.