Both players require surgery after suffering injuries in the 1-1 draw at Leicester City on Saturday.
Midfielder Fer has ruptured his Achilles tendon, while striker Bony has torn his anterior cruciate ligament.
Swansea confirmed the news on their website, adding: "Both players will be assessed further in the week and an update will follow. Everyone at the Swans wishes both players speedy recoveries."
The result against the Foxes at the King Power Stadium lifted Swansea out of the bottom three.