Gomez was initially ruled out for up to six weeks and is expected to feature again this season but Liverpool have put no timescale on his return.
"It's a blow for the boy and for us - because prior to the injury he was in such fantastic shape," Liverpool manager Juergen Klopp told the club's website.
"But he is too valuable to take any risk with, both for our present and future, so we get this procedure done and he comes back when he's ready.
"His attitude during this rehab has been outstanding but it just hasn't healed as we'd have liked so we will make this intervention and then he will come back."
Gomez, who began the season as Klopp's first choice to partner Virgil van Dijk at the heart of the Liverpool defence, has made 18 appearances in all competitions.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
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