The Netherlands captain was taken off at half-time of Monday's defeat at Brentford and further assessment has determined the severity will keep him out for a while.
"It was a surprise for us and a big blow. The diagnosis was pretty harsh and we talk about weeks, more than a month," said manager Jurgen Klopp.
"It's a muscle thing - nothing different to say - it was one sprint too much in that moment.
"For Virgil, it is hard for him but he played an incredible amount of games over the last years and we cannot use him on the pitch, only off the pitch, and we will do that.
"He never had an issue with muscles before and it just now happened. That's how it is. We did nothing different."
Meanwhile Jordan Henderson is set to be available for selection again for the FA Cup clash with Wolves after missing the last match with a concussion.
Klopp: "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."