Curfew will begin at 11pm and end at 5am, Governor Andrew Cuomo announced.
On-duty police officers will also double to 8,000, a massive surge to the streets from the nation's largest policing force.
The escalation follows several nights of protests across the city, with as many as eight demonstrations held in one day, calling for justice in the killing of Mr Floyd and an end to police violence that has brutalised communities.
Governor Cuomo said he supports the protests but condemns the "people who are looking to distract and discredit this moment" with "violence and looting".
"While we encourage people to protest peacefully and make their voices heard, the safety of the general public is paramount and cannot be compromised," he said.
Scheduled protests this week include vigils for Mr Floyd and other victims of police violence, as well as a prayer-focussed protest through Brooklyn led by local church leaders, among other events.
Mayor Bill de Blasio said the curfew is aimed at protecting against "violence and property damage" after several New York Police Department vehicles were torched and dozens of people were arrested, including the mayor's daughter, while widely shared footage from across the city captured police provoking and threatening crowds, driving into them, swatting them with batons and spraying them with pepper spray.
Earlier on Monday, the mayor said officials "have not believed a curfew is the right strategy" but considered implementing one after speaking with the governor and NYPD Commissioner Dermot Shea
"A curfew is not a silver bullet, by the way," the governor said.
It was not clear whether the curfew would apply to essential workers and members of the press or how officers would enforce the measure. The mayor's press office did not immediately respond to The Independent's request for clarification.