Van Dijk sustained the injury in Liverpool's 2-2 draw against Everton in the Merseyside derby on Saturday following a challenge by goalkeeper Jordan Pickford, which went unpunished by match referee Michael Oliver and VAR officials.
The defender was able to walk off the pitch but Liverpool confirmed that he suffered an anterior cruciate ligament injury on Sunday and faces months out of action.
"I'm now fully focused on my recovery and will do everything I can to be back as soon as possible," Van Dijk wrote on social media on Sunday.
"Despite the obvious disappointment, I'm a firm believer that within difficulty lies opportunity, and with God's help I'm going to make sure I return better, fitter and stronger than ever before.
"In football, as in life, I think everything happens for a reason and it's important to try and keep level-headed whether going through the highs and lows.
"With the support of my wife, kids, family and everyone at Liverpool, I'm ready for the challenge ahead."
Liverpool sources have told ESPN that a timescale on Van Dijk's recovery period is impossible to gauge until the player has undergone surgery, but sources are reluctant to rule out a return this campaign.
Van Dijk has been influential for Liverpool since his £75 million move from Southampton in 2018.