Video report by ITV News Washington Correspondent Robert Moore
Public Safety Commissioner John Harrington said state investigators arrested Derek Chauvin, who was one of four officers fired this week, but he did not provide details.
Mr Floyd, who was 46 years old, died on Monday in Minneapolis, Minnesota, after Chauvin was filmed kneeling on the handcuffed man's neck for at least five minutes while arresting him for allegedly using a counterfeit $20 note in a shop.
Chauvin, who was sacked following Mr Floyd's death, has now been charged with third-degree murder and manslaughter, prosecutors said.
The distressing video showing Mr Floyd, who was shirtless and unarmed, being pinned down to the ground while pleading and saying he could not breathe has sparked thousands of protesters to take to the streets.
News of the arrest came moments after Minnesota Gov Tim Walz acknowledged the "abject failure" of the response to this week’s protests and called for swift justice for officers involved.
Mr Walz said the state would take over the response to the protests and that it is time to show respect and dignity to those who are suffering.
"Minneapolis and St. Paul are on fire. The fire is still smouldering in our streets. The ashes are symbolic of decades and generations of pain, of anguish unheard," Mr Walz said.
He added: "Now generations of pain is manifesting itself in front of the world - and the world is watching."
The governor cited a call he received from a state senator who described her district "on fire, no police, no firefighters, no social control, constituents locked in houses wondering what they were going to do. That is an abject failure that cannot happen".
His comments came the morning after protesters torched a police station that officers abandoned during a third night of violence.
Livestream video showed protesters entering the building, where intentionally set fires activated smoke alarms and sprinklers.
Mr Trump also blasted the "total lack of leadership" in Minneapolis.
Now the protests have spilled over into violence. There have been scenes of chaos in multiple cities, from Denver to Los Angeles to New York.
On Friday morning, nearly every building in the shopping district around the abandoned police station had been vandalised, burned or looted.
National Guard members were in the area, with several of them lined up, keeping people away from the police station.
Dozens of fires were also set in nearby St Paul, where nearly 200 businesses were damaged or looted.
Protesters enter and burn down Minneapolis police station
Protests spread across the US, fuelled by outrage over Mr Floyd’s death, and years of violence against African Americans at the hands of police.
Demonstrators clashed with officers in New York and blocked traffic in Columbus, Ohio, and Denver.
The Minnesota State Patrol arrested a CNN television crew early on Friday as the journalists reported on the unrest.
While live on air, CNN reporter Omar Jimenez was handcuffed and led away.
It did not appear that State Patrol authorities gave the CNN crew a reason why they were arrested.
Footage shows the team being led away in handcuffs - leaving their camera rolling live on the streets where protesters had been earlier that night.
Attorney Ben Crump, who is representing members of Mr Floyd’s family, called for an independent investigation, and said he asked to take custody of Mr Floyd’s body to have an independent autopsy performed.
Mr Crump said that talk of a heart condition or asthma are irrelevant because Mr Floyd was walking and breathing before his contact with police.