Liverpool said "no timeframe has been placed" on Netherlands international Van Dijk's return.
Returning to action after ACL surgery can take several months.
Jurgen Klopp's side have since lost Fabinho, who had been deputising in defence for Van Dijk, to a hamstring injury.
A statement from the club released on Friday morning read: "Virgil van Dijk has undergone surgery on the knee ligament injury he sustained earlier this month.
"The Liverpool defender's planned operation took place in London and was conducted successfully.
"Van Dijk will now immediately focus on the beginning of his rehabilitation with the support of the Reds' medical department.
"No timeframe has been placed on the Dutchman's return to action."