The influential centre-back was withdrawn at half-time of Monday’s dismal 3-1 Premier League loss at Brentford due to feeling an issue in his hamstring.
Though the problem was played down initially, it quickly proved to be worse than first feared and Van Dijk was required to visit a specialist to determine the severity.
Liverpool boss Jurgen Klopp has since revealed that the Dutch defender will miss between a few weeks and potentially more than a month with the injury.
“It was a surprise for us and a big blow,” he said at a press conference held before Saturday’s FA Cup tie with Wolves, which is followed by Premier League meetings with Brighton and Chelsea. “The diagnosis was pretty harsh and we talk about weeks, more than a month.”
He added: “It’s not a short-term and I had longer-term injuries as well in my career as a manager. So, it’s somewhere in between. He will be out for a few weeks, definitely.”
But Klopp has confirmed that new signing Cody Gakpo will be in contention to make his debut against Wolves in the third round at Anfield, while captain Jordan Henderson is also nearing a return from a concussion.
Liverpool remain without the likes of long-term absentees Luis Diaz, Diogo Jota and Arthur Melo, however, with Roberto Firmino and James Milner also still doubts.
"Yes, he is in contention. He will be involved in the squad, of course. How exactly we will have to decide in the next few hours, but that's fine,” Klopp said on Gakpo, who was not registered in time to play on Monday but later received the necessary documentation and has joined in with training with his new team-mates at Kirkby.
"First impressions of him are brilliant. With all these things, injured strikers and stuff like this, then you see a guy who is obviously a natural footballer on the pitch and knows where the goal is, it is a lift for everybody.
"So, that's cool and somehow he will be involved, definitely."
On Henderson, who missed the loss at Brentford, Klopp added: "He did exactly what he was allowed to do yesterday – big parts of team training without heading. And from today on, I think he's completely allowed to do everything."