The No.4 was forced off at half-time during Monday's Premier League fixture at Brentford with a muscle complaint.
Offering an update on Van Dijk's fitness, Klopp told Liverpoolfc.com: "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."
However, Jordan Henderson is expected to be available for selection again after sitting out the last match with a concussion.
Klopp said at his pre-match press conference: "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."