The Reds did not provide a timeline for his return.
"Following surgery, Van Dijk will begin a rehabilitation program with the club's medical team to enable him to reach full fitness as soon as possible," read a statement from the Reds.
Though Liverpool revealed few specifics about the ailment, James Pearce of The Athletic reports that Van Dijk injured his ACL and could miss the remainder of the season.
The Dutch center-back was injured early in the 2-2 draw against Everton when he was on the receiving end of a reckless challenge from goalkeeper Jordan Pickford, who escaped the incident without punishment after Van Dijk was ruled offside on the play.
"It was a clear penalty I saw and then we saw the flag went up. I thought they would still look at the foul but that didn't happen," manager Jurgen Klopp said of the VAR after the match, according to BBC. "I don't want to say Jordan Pickford wanted to do it, but it is not a challenge how a goalie can do in the box."
Van Dijk's absence will likely force Klopp to rely on Joe Gomez and Joel Matip in central defense for large stretches of the season. Brazilian midfielder Fabinho, who has lined up as part of the backline before, may see some time at center-back as well.
The injury also puts Van Dijk's availability for Euro 2020 - scheduled to begin in June of next year - in doubt, dealing a potentially massive blow to the Netherlands' hopes of making a deep tournament run.