Hummels has been a key figure in the Germany backline throughout the tournament, and the defender was particularly impressive in the 1-0 quarter-final win over France on Friday.
After putting his team in front with a well-placed 12th-minute header - his second goal of the finals - Hummels was a rock at the back, continually neutralising the threat of Karim Benzema and the rest of the France team.
Klopp, who works with Hummels on a day-to-day basis at Dortmund, was full of praise for the 25-year-old.
"Mats Hummels' performance was extraordinary," he said. "Not only against France, the whole World Cup.
"He is one of the best German players along with Manuel Neuer and Thomas Muller, in terms of shape and performance.
"We are very proud of that. We already knew it, now everybody has seen his outstanding ability.
"His goal was excellent and important, like his first goal against Portugal. Perfect."
Germany's victory set up a semi-final with hosts Brazil on Tuesday, and Klopp knows Joachim Low's men are in for a tough test, despite the absences of Neymar and Thiago Silva.
"There is a good chance for Germany, independent of the terrible story of Neymar's injury," he said.
"Thiago Silva is banned but there will be good alternatives. So it will be an open game.
"Brazil is the home favourite and it is even more difficult for Germany. But they are more consistent in this tournament. So there is good chance for Germany."
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