The Dutchman, who joined the Reds for a world-record fee for a defender in January from Southampton, was a surprise omission from the XI, and Klopp discussed his condition pre-match, per the club website:
"[He is] a little bit injured—not really serious but too much. It was immediately after the game [against Everton] he felt a little bit. We made an assessment.
"If it's the last game of the season maybe you take the risk but it's not the last game of the season obviously. That's why we can't take the risk."
Van Dijk missed much of 2017 due to injury issues, although he returned to the Southampton side early in the campaign and has been fit since.
The Reds finally landed the centre-back in January having failed to get a deal done in the summer. Van Dijk enjoyed a dream debut as he netted a late winner in the FA Cup third-round clash against local rivals Everton.
Klopp called on Dejan Lovren and Joel Matip at the heart of defence for the visit of City. Joe Gomez can also fill in in the position, while Ragnar Klavan is another alternative.