Investigators in the southwestern town of Trollhattan said they based their assumption on items found at the home of the 21-year-old man, who was killed by police, including "his attire, his behaviour at the scene of the crimes", and his choice of victims.
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"Everything gives the impression that the perpetrator acted because of racist motives when he committed his crimes at the Kronan school," police said in a statement.
Identified in the Swedish media as Anton Lundin-Pettersson, a native of Trollhattan, the assailant went from classroom to classroom at the school for six to 15-year-olds, which had many immigrants.
He killed one teacher and a student, and injured another teacher and student who both remained in hospital on Friday.
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Police shot the attacker at the school and he died of his injuries in hospital several hours later.
Wearing black clothes and a Darth Vader-like mask - school children initially thought it was a prank or a Halloween costume - the assailant "chose his victims based on their ethnic background," police investigator Niklas Hallgren told Swedish television SVT.
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