Tim Walz and the Minnesota Department of Human Rights announced the filing of the formal complaint at a news conference Tuesday afternoon.
Widely seen bystander video showing Floyds death has sparked sometimes violent protests around the world.
"And the reason I know it is we saw the casual nature of the erasing of George Floyds life and humanity.
The Minnesota Department of Human Rights enforces the states human rights act, particularly as it applies to discrimination in employment, housing, education, public accommodations and public services.
Arradondo himself was among five black officers who sued the police department in 2007 over alleged discrimination in promotions, pay, and discipline.