Bony limped off just before half-time in the 1-0 Group A loss, having pulled up clutching the back of his right leg chasing a long ball.
With Michu also currently sidelined, due to an ankle problem, the injury comes at a less than ideal time with a daunting trip to Manchester City lying ahead for Michael Laudrup's men on Sunday.
The Swansea boss said: "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."
Swansea also lost right-back Angel Rangel with a calf problem, but Laudrup does not believe his injury is as serious as Bony's.
The defeat to Valencia, who registered the only goal through Daniel Parejo after a deflected Juan Bernat strike fell to him in the box, means Swansea's quest to secure a place in the knockout stages of the competition will go down to the wire.
A point would have been enough to send Swansea through with a game to spare, but instead they must wait until their final game against St Gallen to decide their fate.
Laudrup's side are three points clear of third-placed Kuban Krasnodar, with the Russians having to go to group winners Los Che in the final round and Swansea three goals better off.
But Swansea would have secured the draw they needed had the Italian officials not made a major error just moments after Alvaro Vazquez had replaced Bony.
The Spaniard netted from close-range after Valencia keeper Diego Alves had parried Jonjo Shelvey's volley from an Angel Rangel cross.
However, the assistant referee raised his flag to the fury of the home players, with replays showing Shelvey and Vazques were onside.
It would have done little for Laudrup's mood, with the Dane still nursing a grievance over the late penalty his side conceded in the recent 3-3 draw with Stoke.
"I have watched it a few times," he said. "When Shelvey is going he keeps his flag down, it is when Alvaro scores he puts it up, but he is at least a yard onside."
He ruefully added: "I can't really talk about referees."
But Laudrup insisted he was not concerned that his side's bid for the knockout stages has gone down to the last game, having opened this Group A campaign with a famous 3-0 win at the Mestalla.
"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 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."
Valencia coach Miroslav Djukic was pleased to pick up a positive result after an unsettling few days following the appointment of sporting director Francisco Rufete and the new man's decision to start recording the Serbian's training sessions.
He said: "We are very happy especially in this situation. We needed a win to get our confidence back
"We need to learn how to suffer in games, we played a very good team who came at us in the second half and we coped well.
"I am very happy for the players and everyone at the club."
He added: "I think Swansea are a great team and will qualify, from the start of the group I thought Valencia and Swansea would qualify."
Source: PA
Source: PA