Tens of thousands of people were without power in Manhattan on Saturday evening, ConEdison said.
There were 42,000 customers without power in New York, most of them in Midtown Manhattan and the Upper West Side, the utility company said.
Mayor Bill de Blasio, who was campaigning for president in Iowa, said it appears the outage was the result of a mechanical problem in the electrical grid.
"This appears to be something that just went wrong in the way that they transmit power from one part of the city to another," he told CNN. "It sounds like it is addressable in a reasonable amount of time."
The city's fire department was responding to numerous transformer fires, the first of which occurred in Manhattan on West 64th Street and West End Avenue, officials said.
Several Broadway and off-Broadway shows said they were canceling performances, according to tweets aggregated by The Broadway League.
Firefighters were also responding to people trapped in elevators and subway cars, and they are operating all over Manhattan's West Side from streets in the 40s to the 60s, according to an FDNY spokesman.
The outage was having a widespread effect on the New York subway system, which was experiencing power outages in its stations, the agency managing the trains said.
"We're working to identify causes and keep trains moving," the Metropolitan Transportation Authority tweeted.
The outages were affecting "multiple lines," the MTA said. It advised people to stay away from below-ground stations.
It told one Twitter user there were extensive delays on many lines.
The lack of power was a major issue on the streets and in buildings, too.
A CNN producer on the Upper West Side said he was at a movie when the theater went dark at about 7 p.m. He went outside and saw traffic and street lights were out. Traffic was jamming up in intersections but it wasn't gridlocked, he said.
Twitter user Sahid Abraham posted a photo from Times Square that showed some of the famous electronic billboards dark.
Another user posted a photo showing a man at 66th Street and Broadway directing traffic.
The outages come 42 years to the day of an extensive blackout that affected much of the city.