According to Fox Sports, citing beIN Sports, van Dijk was diagnosed with a cruciate ligament rupture.
It is noted that the 29-year-old Dutchman will need about seven to eight months to recover, and thus he will miss the rest of the season.
The defender was injured already in the 11th minute of the Merseyside derby with Everton, colliding with the rival goalkeeper Jordan Pickford, after which he left the field.
Van Dijk has been playing for Liverpool since 2018.
He has 130 appearances for the Merseysides in all tournaments, in which he scored 13 goals and gave six assists.
Earlier it was reported that Everton and Liverpool drew in the Premier League's Merseyside derby.