The Ivorian striker, the Swans' record signing, suffered a hamstring injury while on Europa League duty on Thursday.
He was forced out of the action at the Liberty Stadium shortly before half-time, preventing him from helping the hosts to offer a response to a Dani Parejo strike - which proved to be the match-winner.
Bony pulled up clutching the back of his right leg after chasing a long ball.
His absence heading into the busy festive period will be keenly felt by Swansea, with Laudrup already shorn of the services of Spanish hit-man Michu due to an ankle complaint.
He said on Bony the defeat to Valencia: "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.
"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."
Defeat for the Swans on home soil prevented them from booking their place in the last-32, but Laudrup claims taking matters to the final round of fixtures offers no great concern.
"I know in European competition you have to play until the last game and I knew from the beginning that it would be very difficult," he said.
"Today we saw a Kuban side who everyone thought was the weakest in the group win 4-0 at home against St Gallen.
"It is not easy and you have to play until the last game.
"Tonight I think Valencia were the better team in the first half and dominated in midfield, not that they created many chances.
"We had a disallowed goal but Alvaro (Vazquez) was at least one yard onside.
"In the second half we took over and had three or four chances but had one saved on the line and couple of others that very close.
"Maybe we will have to get that last point in Switzerland."