The British record $US170 million (STG126m) signing was injured in a tackle while scoring the opening goal in Saturday's 2-1 win against Tottenham in the Premier League and limped off.
Isak's absence will not only impact Liverpool's campaign but possibly Sweden's chances of qualifying for the World Cup. Sweden face Ukraine in the European playoffs in March when the semi-finals take place.
"After diagnosis, an operation was completed today on an ankle injury that included a fibula fracture," Liverpool said in a statement. "Isak's rehabilitation will now continue at the AXA Training Centre, with no timeframe yet placed on his return."
Isak's injury is the latest blow in what has been a troubled season for the 26-year-old forward.
A protracted move from Newcastle in the summer meant he eventually arrived at Liverpool in September having not had a full pre-season to prepare for the new campaign.
He was gradually eased into Arne Slot's team as he regained full sharpness but then a groin injury kept him out of the Liverpool lineup for another month. In all, he has made just 10 starts for the Premier League champions and scored three goals.
Slot is already without Mohamed Salah, who is at the Africa Cup of Nations and will hope Hugo Ekitike continues to carry the goal-scoring burden in the meantime.
The France international, who was another recruit this season, has 11 goals so far for his new club, including one against Tottenham. He has scored five in his last three league games and has the chance to establish himself at the point of Liverpool's attack.
Liverpool are on a six-game unbeaten streak after the Merseyside club's title defence unravelled from September to the end of November.
A remarkable run saw Slot's team lose six out of seven games in the league and tumble down the standings.
But after back-to-back wins against Brighton and Tottenham they are up to fifth and level on points with Chelsea in fourth.
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