Norway finished top of group B with the Germans as runners-up. In the group's other game, Iceland beat Netherlands 1-0 to knock out the Dutch and qualify for the last eight as one of the best third-placed teams.
Seven-times champions Germany increased the pressure in the second half but despite a slew of corners and free-kicks they were kept at bay at the Kalmar Arena.
In Vaxsjo, Iceland went ahead on the half-hour when an unmarked Dagny Brynjarsdottir headed home a deep cross from Hallbera Gisladottir to score Iceland's second goal of the tournament.
Despite having 22 shots on goal, the Dutch could not find a way past Gudbjorg Gunnarsdottir in the Icelandic goal.
Norway won the group with seven points. Germany and Iceland finished on four points, with the Germans securing second place thanks to their superior goal difference.
Netherlands earned a single point from their draw against Germany, but failed to score.