The centre-back damaged knee ligaments following an incident involving Blues goalkeeper Jordan Pickford after six minutes at Goodison Park.
Van Dijk was required to be substituted and further assessment on the injury has revealed an operation will be needed.
No specific timescale is being placed upon his return to action at this stage.
Following surgery, Van Dijk will begin a rehabilitation programme with the club’s medical team to enable him to reach full fitness as soon as possible.