The Dutchman was replaced by Joe Gomez after 54 minutes against his former club, prompting fears across Anfield that he could face a prolonged spell out.
Clutching his rib as he left the field, Van Dijk headed down the tunnel for treatment, but soon emerged alongside Xherdan Shaqiri in the dugout.
With Liverpool to play Chelsea in back-to-back games on Wednesday and next Saturday, and a trip to Napoli to come the following Wednesday, any absence for the 27-year-old could be costly.
But speaking after his side’s historic seventh win in a row, Klopp allayed concerns over Van Dijk’s fitness.
“He had a bruise on his ribs before the PSG game, today he got another hit there,” he explained.
“It should not be too serious. He said he could not shout more—which is 60 percent less!
“He should be absolutely OK.”
In more positive news, Gomez’s performance alongside Joel Matip, up against the Saints’ most troublesome player in Nathan Redmond, was hugely encouraging.
The hope is that Van Dijk will be fit to return for next weekend’s title clash with the Blues in the Premier League.