“Clint is one of our most experienced players and ready to assume a more vocal leadership role,” Klinsmann said in a statement.
“He has been huge for us in World Cup qualifying so far and is already one of our key leaders. We know he will do a great job for these two important games.”
Dempsey, who has captained his country on one other occasion during his 92-game international career, replaces Carlos Bocanegra who was not selected due to his lack of game time at club level with Racing Santander.
Everton goalkeeper Tim Howard, who has stood in for Bocanegra in the past, was unavailable for the two-match spell because of injury.