Isak suffered the injury, which included a fractured fibula, as he scored Liverpool's opening goal in Saturday's 2-1 win over Tottenham Hotspur, when his foot got caught between Micky van de Ven's legs as the defender dived to block his shot.
"Alexander Isak today successfully underwent surgery on the injury he sustained on Saturday," Liverpool said. "After diagnosis, an operation was completed today on an ankle injury that included a fibula fracture. No time frame (is) yet placed on his return."
Liverpool smashed the British transfer record to sign the 26-year-old Sweden international for 125 million pounds in September after Isak made it clear he wanted to leave Newcastle United and was frozen out of the squad.
Isak, who scored 54 Premier League goals in 86 games for Newcastle, made his debut against Atletico Madrid in the Champions League after a lack of fitness kept him out of the first league game after his arrival.
He has struggled in a Liverpool side that have failed to replicate last season's title-winning form and has scored two league goals in 10 appearances.
Isak netted his first goal for the club in a League Cup win over Southampton in September and has failed to find the net in his five Champions League appearances.
Liverpool, fifth in the standings and 10 points behind leaders Arsenal, were already without Mohamed Salah, who is on Africa Cup of Nations duty with Egypt.
They will now have to rely heavily on striker Hugo Ekitike, another new signing who has scored eight league goals, including five in the last three games, and may need to invest in the January transfer window with Salah's future at the club in doubt.
