The outage was having a widespread effect on the NY subway system, which was experiencing power outages in its stations, the agency managing the trains said.
Power was out in much of Rockefeller Center.
Freddi Goldstein, a spokeswoman for Mayor Bill de Blasio, who was campaigning in Iowa for president, said that the mayor had been briefed on the blackout and that the Office of Emergency Management was responding.
An update from ConEd at 8.08pm read: 'We are working to restore power to 42,000 customers primarily in the Westside of Manhattan'. "It sounds like it is addressable in a reasonable amount of time".
On Twitter, Con Edison described the outage as "extensive".
The Twitter account for NY subways said the agency is working to keep trains moving and will bypass affected stations. The MTA is working with Con Edison to determine the cause.
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Power went out at Madison Square Garden just before 9:30 p.m., the site of a Jennifer Lopez concert.
Hearst media group producer, Derek Turner, also took to Twitter to share a picture of a man directing traffic after the street lights went out.
"We were stuck for about 75 minutes", Jeff O'Malley, 57, told Reuters news agency.
The casts of Broadway's "Come From Away" and "Waitress" did the same as people captured the offstage performances with their camera phones.
Twitter user Lizzy Aimée shared a video of firefighters entering her apartment building and wrote: 'Can't get up to our apt and people are stuck in the elevators!'