The cause of the blast late on Saturday in Chelsea remains unclear. Mayor Bill de Blasio described it as “intentional” but said that there were no known links to terror.
The force of the blast blew out windows and could be heard several blocks away.
Another device, reportedly a pressure cooker rigged with wires, was later found in the same district.
None of the injuries is life-threatening but one is serious, New York’s fire commissioner said.
Most of those hurt suffered cuts and other minor injuries from glass and other debris.
The explosion occurred around 21:00 (01:00 GMT on Sunday). Witnesses said people ran in all directions following the “incredibly loud” blast.
Unconfirmed reports said the blast went off in a dustbin. Several blocks have been closed down by police.
“The initial indications is this was an intentional act,” Mr de Blasio said.
But he added: “We also want to be upfront saying that there is no evidence at this point of a terror connection to this incident.”
Law enforcement officials said that the device found at the second Chelsea location appeared to be a pressure cooker attached to wiring and a mobile phone. Police said it had been removed safely.
Chelsea is among the most fashionable districts of Manhattan and its bars and restaurants are usually crowded at the weekend.
President Barack Obama is being kept up to date on the investigation, a White House official said.
“Obviously we need to do everything we can to support our first responders and pray for the victims,” she said.
“I’ll have more to say about it when we actually know the facts,” she added.
Speaking at a rally in Colorado before police had commented on the cause of the blast, Republican presidential candidate Donald Trump told supporters that a “bomb” had gone off.
He said: “Nobody knows exactly what’s going on, but boy, we are living in a time – we better get very tough, folks.”
The blast comes after a pipe bomb explosion in neighbouring New Jersey hours earlier along the route of a planned charity race.
No injuries were reported, and Mr de Blasio said there was no evidence of a link.
On Tuesday President Obama and other world leaders are due to attend the UN General Assembly in New York.