Bony was forced off late in the first half of the 1-0 loss at the Liberty Stadium after grabbing at the back of his right leg in pain while chasing a long ball.
With Spanish striker Michu also sidelined due to an ankle problem, Bony's injury is a major blow for Swansea boss Michael Laudrup ahead of Sunday's trip to in-form Manchester City.
"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," Laudrup said.
"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."