With the Reds 3-0 up, the Dutch centre-back was involved in a challenge with Shane Long in the 51st minute and came away holding his side.
Van Dijk was unable to continue and had to be subbed off four minutes later, with Joe Gomez coming on in his place.
However, Reds manager Jurgen Klopp expressed his confidence that the injury is unlikely to keep the influential Van Dijk on the sidelines for too long.
“He already had a bruise in the ribs before the PSG game, which is very uncomfortable and today he got another hit there," said Klopp.
“It’s not cool but should not be too serious.
"He said he couldn’t shout anymore, so that’s obviously 60 per cent less of his level!
"It should be absolutely OK, hopefully. I didn’t hear anything different."
Van Dijk was seen on the bench later in the second half rather than in the dressing room receiving treatment.
The Reds went on to win the match 3-0, with the club setting a record for their best start to a season in club history.
It is expected that Van Dijk will be available for the Premier League clash with Chelsea, but will sit out the League Cup fixture.