Van Dijk made his comeback from nine months out after anterior cruciate ligament surgery on his right knee with a 20-minute appearance in the 4-3 friendly defeat to Hertha Berlin on Thursday.
Van Dijk effectively has two more opportunities to get some pre-season minutes in as Liverpool have back-to-back matches against Bologna in Evian next Thursday before two home games against Athletic Bilbao and Osasuna.
"I think we have to be careful and I think Jurgen Klopp will be," Carragher, speaking at a Soccer Aid event, told the PA news agency.
"He's had a really serious injury and he's got to make sure he is not rushed back.
"If he's back to his best he is the best central defender in world football and that's what Liverpool will want over the next five or six years, not the next five or six weeks.
"If he doesn't make the first game of the season it's not the end of the world, it is about making sure Virgil van Dijk is 100 per cent right so he's in a position where he can have the next five or six years at Liverpool at a top level.
"It may be a gentle start with Virgil until we see him when he is 100 per cent right, but if that could be on that first game of the season and he can play the next few games I think everyone would be delighted."
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