The 46-year-old died on Monday in Minneapolis, Minnesota, after police officer Derek 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.
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.
Police let off rubber bullets, tear gas and concussion grenades, some of which members of the crowd threw back, as looting also broke out.
As the violence escalated, a man was shot dead near the scene of protests.
The man was found lying on the pavement at around 9.30pm with a gunshot wound and was taken to hospital, where he later died. A suspect has been arrested.
Fires erupted after dark at several businesses, including a car parts store, with eyewitnesses claiming the fires appeared to have been started deliberately.
Images from American television news from a helicopter over the area also showed dozens of people looting a Target store, running out with clothing and shopping trolleys full of merchandise.
Protests over Mr Floyd's death have also now spread to Los Angeles.
Minneapolis Police Director of Communication, John Elder, said thatbeyond the shooting, there were no known injuries to protesters or police, and no additional arrests.
"Tonight was a different night of protesting than it was just the night before," Elder said.
He said officers performed CPR and first aid on the victim, close to the scene of the protests.
Mr Elder said "two officers arrived, one began CPR immediately while the other officer really kind of held the scene and ensured safety."
He added: "This was close to the area of protests. And there were a number of people that were there that were not cooperating with officers."
Mr Floyd's death on Monday night is currently being investigated by the FBI and state law enforcement authorities, US President Donald Trump has confirmed.