Tim Walz and the Minnesota Department of Human Rights announced the filing of the formal complaint at a news conference Tuesday afternoon.
The FBI is also investigating whether police willfully deprived Floyd of his civil rights.
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.
The Minneapolis Police Department has faced decades of allegations of brutality and other discrimination against African Americans and other minorities, even within the department itself.
Arradondo himself was among five black officers who sued the police department in 2007 over alleged discrimination in promotions, pay, and discipline.