Germany won 1-nil thanks to a scrappy goal after a corner in the first half in front of some 9,000 spectators in the southern city of Växjö.
Widely tipped to win the tournament, Germany play hosts Sweden on Wednesday, after Sweden beat Iceland 4-nil in the other quarter final played on Sunday. Germany beat Sweden in the final of the Women's Euros in 2001.
Meanwhile, an animal rights group has reported the Iceland team for animal cruelty to Swedish authorities, after players reportedly threatened to flush their team mascot - a goldfish named Sigurwin - down the toilet following their loss against Sweden.
The local authority that received the complaint has since issued a statement saying that it will not be carrying out an investiagtion into the complaint.
According to the Swedish TT news agency, local media reports that Sigurwin will be handed over to a pet shop in the southern city of Malmö.