Midfielder Fer suffered a ruptured Achilles tendon in the match at the King Power Stadium while striker Bony tore his anterior cruciate ligament after coming on as a substitute.
Fer, who has played 20 league games this season scoring one goal, was taken off on a stretcher in the first half after going down unchallenged.
Ivory Coast international Bony, a close-season signing from Manchester City, landed awkwardly just moments after coming on in the second half but he played on and left the stadium in a knee brace.
Both players are now expected to undergo surgery, Swansea said on their website (www.swanseacity.com) on Sunday.
"Both players will be assessed further in the week and an update will follow," the club said.
Swansea are 17th in the Premier League with 24 points, having moved out of a congested relegation zone on goal difference.
(Reporting by Toby Davis; Editing by Catherine Evans)
