There were precedents, she said, including a consent decree approved in Chicago last year after the US Justice Department found a long history of racial bias and excessive use of force by police.
Widely seen bystander video showing Floyd's death has sparked sometimes violent protests around the world.
The officer, Derek Chauvin, has been fired and charged with third-degree murder and second-degree manslaughter. Three other officers involved were fired but have not been charged.
"We know that deeply seated issues exist," the governor said.
"And the reason I know it is we saw the casual nature of the erasing of George Floyd's life and humanity. We also know by the reaction of the community. They expected nothing to happen, and the reason is because nothing did happen for so many times."
Walz said the investigation into the police department's policies, procedures and practices over the past 10 years will determine if the force has engaged in systemic discrimination toward people of colour, and root it out. Lucero will lead the investigation.
All 12 members of the Minneapolis City Council endorsed a statement read by Council President Lisa Bender at a news conference later Tuesday in support of the investigation.
"We urge the state to use its full weight to hold the Minneapolis Police Department accountable for any and all abuses of power and harms to our community, and stand ready to aid in this process as full partners," the council said.
Mayor Jacob Frey said the state's intervention will help break what he called a stalemate on reform.
"For years in Minneapolis, police chiefs and elected officials committed to change have been thwarted by police union protections and laws that severely limit accountability among police departments," Frey said in a statement.
"I welcome today's announcement because breaking through those persistent barriers, shifting the culture of policing, and addressing systemic racism will require all of us working hand in hand."
A police department spokesman and the president of the officers' union didn't immediately respond to requests for comment.
The FBI is also investigating whether police willfully deprived Floyd of his civil rights.
The Minnesota Department of Human Rights enforces the state's human rights act, particularly as it applies to discrimination in employment, housing, education, public accommodations and public services.
Mediation is one of its first-choice tools, but the cases it files can lead to fuller investigations and sometimes end up in litigation.
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.
Critics say its culture resists change, despite the elevation of Medaria Arradondo as its first black police chief in 2017.
Arradondo himself was among five black officers who sued the police department in 2007 over alleged discrimination in promotions, pay, and discipline.
They said in their lawsuit that the department had a history of tolerating racism and discrimination. The city settled the lawsuit for $740,000.
State Public Safety Commissioner John Harrington, who was neighboring St. Paul's second black police chief, said good officers should welcome the investigation.
He co-chaired a working group with Attorney General Keith Ellison that reported back in February on ways to reduce police-involved deadly force encounters.
"I've been a cop for 40 years. I have lived in this system that they're talking about reforming ... The cops I talk to, the cops I've worked with since 1977 to date will tell you, they want change," Harrington said.
"They don't want to work in a flawed system. They don't want to have to be wearing gas masks. They don't want to have to be on riot control duty."
Earlier Tuesday, an attorney for Floyd's family again decried the official autopsy that found his death was caused by cardiac arrest as police restrained him and compressed his neck.
The medical examiner also listed fentanyl intoxication and recent methamphetamine use, but not as the cause of death.
A separate autopsy commissioned for Floyd's family concluded that he died of asphyxiation due to neck and back compression.
"The cause of death was that he was starving for air. It was lack of oxygen. And so everything else is a red herring to try to throw us off," family attorney Ben Crump said.
He said the Hennepin County medical examiner went to great lengths to try to convince the public that what was shown on bystander video didn't cause Floyd to die.
Ellison told ABC's 'Good Morning America' that prosecutors are working as fast as they can to determine whether more charges will be filed.
