Laudrup reveals Bony blow after Valencia loss
The Welsh club missed the chance to book their spot in the knockout stages after Daniel Parejo's strike gave the Spaniards a 1-0 win at the Liberty Stadium.
But there was further concern for head coach Michael Laudrup with Bony forced off just before half-time after feeling a twinge in his right hamstring.
With last-season's leading-scorer Michu also currently sidelined with knee and ankle problems, Swansea could find goals hard to come by ahead of a crucial two-week period for the club.
Asked about Bony's injury post-game, Laudrup said: "It could be quite a serious one.
"We will have to wait two or three days until we get a scan but unfortunately I think we are talking several weeks at least.
"But today we saw Alvaro (Vazquez) have a goal disallowed and one cleared off the line. With Bony's injury, now he has his chance.
"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."
Bony was not the only injury concern for Laudrup, with right-back Angel Rangel also picking up a calf problem, which could also see him sidelined for a couple of games.
The Swans face four tough matches in the next 12 days, starting with a clash with free-scoring Manchester City in the Premier League on Sunday.
They must now also travel to St Gallen in Switzerland on December 12 and come away with at least a point to ensure progression to the last 32 in the Europa League.
Despite being outplayed in the opening half, Swansea had a right to feel aggrieved not to have been awarded an equaliser when Vazquez struck on the stroke of half-time only to have it controversially chalked off for offside.
Speaking on the defeat to the Spaniards, Laudrup said: "Valencia were the better team in the first half. They dominated the midfield. Not that they created many chances but they did dominate the first-half.
"We had a disallowed goal, which I think we all saw that, unfortunately for us, was given offside when he was at least a yard on.
"I saw that the linesman, when Jonjo (Shelvey) touches the ball, keeps his flag down. When Vazquez touches the ball, he puts his flag up but he is at least a yard onside.
"I think we took over in the second half. We had three or four chances – one saved on the line and a couple of others went very close.
"Now, we just have to get that last point in Switzerland. They are out of the competition but they will want to win."