A Reuters witness in the area reported hearing an explosion at about 7 p.m. (2300 GMT), and a New York City Fire Department spokesman said firefighters were on the scene of a transformer fire.
Media reports indicate that thousands are without power in parts of Midtown Manhattan and the Upper West Side.
The Metropolitan Transportation Authority tweeted that there were outages at various underground stations.
NBC News correspondent and anchor, Kate Snow, tweeted a picture of a dark hallway at the network's headquarters, and said staffers were forced to use backup generators to broadcast Saturday's edition of Nightly News.
Mayor Bill de Blasio, who was campaigning for president in Iowa on Saturday, tweeted that the police and fire departments and other city agencies were working to respond a manhole fire that caused the outage.
The utility Con Edison said that about 42,000 customers were without power, mainly on the West Side.
'Several stations are now without power and are being bypassed by all trains, ' it posted on Twitter.
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The New York City transit system said it was working with Con Ed to restore power in affected subway stations.
ConEd said on Twitter: 'We are responding to extensive outages on the Westside of Manhattan.
The outage also saw some Broadway shows cancel their Saturday evening performances, including Best Musical Tony victor Hadestown and King Kong.
Across the city, as traffic lights went down, New Yorkers took the situation into their own hands and began directing traffic.
Twitter user @MarlinPie shared a video of performers outside Carnegie Hall.
A Jennifer Lopez concert at Madison Square Garden was halted and disappointed fans had to be evacuated.
"We're trying to get people out of subways".
New Yorkers are also calling for help through social media, as at least one person has been trapped in an elevator by the outage. The power was gradually restored throughout the next day.