The Reds say no specific timescale is being placed upon his return to action at this stage.
The influential defender was absolutely clattered by Everton 'keeper Jordan Pickford in just the sixth minute of the 2-2 draw at Goodison Park on Saturday forcing the 29-year-old to be replaced, with the England number one inexplicably not receiving any kind of punishment whatsoever.
The club has yet to set a date for Van Dijk's surgery due to the necessity for the swelling around the knee joint to subside sufficiently for the player to be operated on.
Liverpool did not give a timescale on Van Dijk's absence, but an injury of that nature will likely keep the Netherlands worldwide out for a long period.
"I felt at the start of the season that Liverpool were still the team to beat".
"I know the transfer window has just finished by they have to be ready on January 1 to bring someone in".
The sidelining of Van Dijk is compounded by the absence of goalkeeper Alisson Becker with a shoulder injury.
The loss of Van Dijk's dominant aerial presence was obvious as Everton scored twice from headers to come from behind in a contentious derby at Goodison Park.
Liverpool, meanwhile, are hopeful that an injury sustained by midfielder Thiago Alcantara against Everton does not prove to be serious.
Thiago eventually got up from Richarlison's red-card challenge and was able to create the opening for Henderson's disallowed goal but later reported an injury and was also sent for a scan on Saturday. "It was not our day but the performance was the performance I wanted to see", said Jurgen Klopp after the game.