In the 11th minute of the Merseyside derby, the Liverpool centre-back made his way into the Everton box to attack a free-kick when he was clattered into by the England international.
The VAR checked the incident for a possible penalty and former Manchester United defender Gary Neville watching the game made his thoughts clear.
However Pickford was saved due to an offside decision against Van Dijk.
Van Dijk was subbed off for Joe Gomez, who was on the bench with Jordan Matip the other starting centre back in Liverpool's XI.
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Virgil van Dijk, Everton v Liverpool
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It is not yet known the extent of the Netherlands international's injury, but it is another blow for manager Jurgen Klopp who is also without goalkeeper Alisson and midfielder Naby Keita.