The striker, a summer signing from Dutch side Vitesse, is sidelined along with Michu, leaving Michael Laudrup short of options in attack ahead of the trip to Manchester City
Bony, who has scored seven goals for the club since joining from Vitesse this summer, was injured in the 1-0 Europa League defeat to Valencia on Thursday.
The striker is due to have a scan to determine the extent of the problem, but Laudrup is anticipating a long absence.
"It could be quite a serious one," Laudrup told reporters. "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."
Laudrup is also without Michu, but is hopeful of having the Spain international return to action in the coming weeks.
He added: "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."