The defender scored the only goal of a match neither team ever took control of when he headed in a free kick from Toni Kroos after 13 minutes.
In a game of few clear chances, Germany keeper Manuel Neuer denied France a shot at extra time when he blocked Karim Benzema's effort.
Germany, the first country to qualify for four successive semi-finals, will meet either hosts Brazil or Colombia in the semi-final next week. The South Americans meet in the second quarter-final of the day in Fortaleza (2000GMT).
Joachim Loew's side will have to play much better than they did against France to reach their first final since 2002.
Germany went ahead when they won a free kick on the left after Paul Pogba fouled Kroos who took the free kick himself and swung a perfectly flighted ball towards Hummels.
The center back launched himself at the ball and held off defender Raphael Varane in the same movement and powerfully flicked the ball in with it grazing the underside of Hugo Lloris's bar for his second goal of the tournament.
France took time to respond but came close to an equalizer in the 34th minute when Mathieu Valbuena shot from close range but was denied by a superb save from Neuer who turned the ball away with his left hand.
Either because of the sun beating down from a cloudless sky or because of the tension of the occasion, neither team played well, although France were particularly poor.
Both made error after error and the game rarely set the pulses racing until the last 15 minutes as France desperately searched for the equalizer that never came.
Substitute Andre Schuerrle should have doubled Germany's lead but his low strike was blocked by Lloris.
source: www.abs-cbnnews.com
