The eighth-seeded Serb Tipsarevic received a treatment on a foot injury and decided to quit when he was trailing 5-1 in the second set. Almagro won the first set 6-2, Xinhua reports.
It is going to be Almagro's first quarterfinal appearance at Melbourne Park after making the last eight three times at the French Open.
Almagro will play against fourth seed Ferrer for a berth in the semifinals, who beat Japan's Kei Nishikori in straight sets.