Isak, signed from Newcastle for a British record US$168 million in September, suffered the injury in the process of scoring in Liverpool’s 2-1 win at Tottenham on Saturday.
The 26-year-old was tackled by Tottenham defender Micky van de Ven and limped off immediately after his goal.
“Alexander Isak today successfully underwent surgery on the injury he sustained on Saturday,” a Liverpool statement said.
“After diagnosis, an operation was completed today on an ankle injury that included a fibula fracture.
“Isak’s rehabilitation will now continue at the AXA Training Centre, with no time frame yet placed on his return.”
Isak’s injury is the latest setback in his disappointing start to his life with Liverpool.
He has scored just three goals in 16 appearances since completing his protracted move to Anfield.
A dispute with Newcastle meant he did not have a proper pre-season programme and arrived at Liverpool well behind his team-mates in terms of fitness.
His season was then interrupted by a groin injury.
Isak’s absence will be a major blow for Reds boss Arne Slot, with Mohamed Salah at the Africa Cup of Nations and Cody Gakpo not ready to return from a muscle injury until early in the new year.
It leaves Slot with Hugo Ekitike, who has five goals in his past four games, and the little-used Federico Chiesa as his only senior forwards. (AFP)