Public Safety Commissioner John Harrington said state investigators arrested the officer, Derek Chauvin.
Chauvin was in the custody of the state's Bureau of Criminal Apprehension, television station Fox 9 KMSP reported following the public safety commissioner's announcement.
The arrest came after three days of protests, which escalated in violence as demonstrators torched a police precinct in Minneapolis that had been abandoned by officers.
The protests were sparked by outrage over the death on Monday of the 46-year-old unarmed black man in the video Monday.
Minnesota governor expects 'swift' justice
Earlier Friday, Minnesota Governor Tim Walz called for an end to the violence that has rocked Minneapolis and said he expected "swift" justice for the officers involved.
Walz also promised a reckoning with the racial inequities behind the unrest, but said that first the state's National Guard would work to restore order following three nights of arson, looting and vandalism in the Midwestern city.
"We have to restore order to our society before we can start addressing the issue," Walz told a briefing, referring to decades of racial divide across the US. "We cannot have the looting and recklessness that went on."
Walz also apologised for the arrest of a black CNN correspondent and his crew who were led off in handcuffs while reporting live on television early Friday close to a police precinct that was burned overnight, saying there was "no reason" it should have occurred.
US President Donald Trump weighed in on the unrest on Friday with incendiary language that prompted Twitter to hide his tweet behind a warning that accused him of "glorifying violence" in violation of its rules.
"These THUGS are dishonoring the memory of George Floyd, and I won't let that happen," Trump said in the tweet. "Any difficulty and we will assume control but, when the looting starts, the shooting starts. Thank you!"
A bystander's mobile phone footage showed Floyd repeatedly moaning and gasping while he pleaded to the officer kneeling on his neck, "Please, I can't breathe." After several minutes, Floyd gradually grows quiet and ceases to move.
Walz said he understood what was driving the protests, saying he believed the community had "lost faith" in the police force and "felt they were part of the problem". But he said Floyd's plight had gotten "lost in 48 hours of anarchy".
More protests were expected in several US cities on Friday and over the weekend.
In New York, protesters are also calling for charges to be brought against a white woman who was recorded calling the police on a black man in a park who asked her to keep her dog on a leash.
(FRANCE 24 with AP and REUTERS)