Three goals in the opening 20 minutes put Sweden on course for an easy victory in blazing sunshine in Halmstad.
Marie Hammarstrom put the Swedes ahead after just three minutes, surging forward before firing a powerful left-footed shot across Iceland goalkeeper Gudbjorg Gunnarsdottir and into the net.
Gunnarsdottir was then at fault for Sweden's second 11 minutes later, rushing out of her goal but beaten to the ball by Josefine Oqvist, who poked it past her to double the lead.
Lotta Schelin netted Sweden's third five minutes later when she showed quick feet to nip in ahead of Gunnarsdottir to deftly turn Kosovare Asllani's pass into the net from close range.
With Sweden cruising, Asllani set up Schelin again in the second half, the Lyon striker netting her fifth goal of the tournament as she toe-poked the ball home just before the hour mark.
In Vaxsjo, Simone Laudehr scored the only goal of the game for Germany in the 26th minute as a clearance from a corner dropped to her and her first-time shot deflected off Italy's Elisa Bartoli and into the net.
The Germans will face Sweden in the first semi-final in Gothenburg on Wednesday.
Norway play Spain and France take on Denmark in the remaining quarter-finals on Monday, with the winners meeting in the second semi-final in Norrkoping on Thursday.
The final will be held at the Friends Arena in Stockholm on July 28.
(Reporting by Philip O'Connor; Editing by Sonia Oxley)
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