The Dutch are favourites to win Group E, but having watched Fabio Capello's England draw on Saturday coach Van Marwijk says the Dutch must be wary of the Danes.
"We have enormous respect for any opponent and especially for Denmark, he said. "We know each other well, there are no secrets between the sides.
"You saw yesterday with England that games which might look easy to win aren't always so, you can't afford to take anything for granted."
The Dutch looked sharp in training on a reduced-sized pitch at Johannesburg's Soccer City stadium, but Bayern Munich winger Arjen Robben trained separately as he continues his recovery from a thigh strain.
The 26-year-old flew into Johannesburg on Saturday and is not expected to face the Danish, but should be in contention for the remaining group games against Japan and Cameroon.
"Robben trained at the (neighbouring) red stadium and is following the same programme as we are, it is much better for him to train on a full-sized pitch," said the Dutch boss.
The Danes have some fitness concerns with a question mark over Arsenal striker Nicklas Bendtner who has been out of action with a groin strain since May, but Van Marwijk says he expects the Gunners' front man to play.
In his own squad, Van Marwijk has plenty of top-quality talent even without Robben with the likes of Arsenal's Robin van Persie, Real Madrid's Rafael van der Vaart and Inter Milan's Wesley Sneijder to choose from.
Much has been said of the Dutch desire to shake off their tag of group phase heroes and knock-out stage zeros as they bid to win their first FIFA World Cup.
Van Persie has said the Oranje must reach at least the semi-final, but Van Marwijk said he was relaxed about his country's biggest game since the EURO 2008 quarter-final defeat by Russia.
"You need a bit of tension before a World Cup game and it is a good to have that sort of tension. It makes you sharper and aloof, but you don't want to overdo it either."