The driver, 34-year-old Isaiah Peoples, reportedly targeted the family solely on their appearance, according to police in Sunnyvale, near San Francisco, who are now treating the case as a "hate crime".
"There is new evidence that Peoples intentionally targeted victims based on their race and belief that they were Muslim," said Sunnyvale Public Security in a statement.
According to local media, three members of the same family are among the eight pedestrians injured Tuesday -- a father and his son and daughter.
The nationality and religion of the family have not been released.
A lawyer for Peoples said the incident "was clearly the result of a mental disorder", and he would seek psychiatric treatment for his client - who he described as a military veteran possibly suffering from post traumatic stress disorder.
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