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Robben has had an outstanding tournament, scoring three goals in five games, providing one assist and regularly causing havoc with his direct running.
Speaking ahead of Wednesday's match in Sao Paolo, Demichelis told Clarin that, once his former Bayern Munich teammate was running at his marker, he was difficult to stop.
He said it was vital for defenders to put in a strong challenge as soon as he received the ball.
"He is a phenomenon -- it is impossible to know which way he is going to go," Demichelis said.
"So you must attack him, because the more you stand off, the closer he brings you to your own goal and you have less chance against him.
"And as he does not like physical contact, you must make him feel it -- you must rough him up. The Dutch players, especially Robben, must feel the Argentine passion."
The Manchester City defender, 33, praised Netherlands coach Louis van Gaal, whom he knows from their days together at Bayern Munich.
"At this moment we are not in touch, but I will always recognise that he is the best when it comes to football, the concepts he manages and what he tries to impose on his team," Demichelis said.
"He is showing that today. I learned so much from Van Gaal."
Arjen Robben or Lionel Messi?
ESPN's Last Call panel discuss Argentina's dependence on Lionel Messi and Netherlands' depends on Arjen Robben.
Key matchups for Argentina, Netherlands
The ESPN FC World Cup Encore panel delve into the key player matchups between Argentina and Netherlands.