The governor of NY state, Andrew Cuomo, said in a statement that although no injuries had been reported, "the fact that it happened at all is unacceptable", and promised an investigation.
The outages come 42 years to the day of an extensive blackout that affected much of the city.
"I'm devastated and heartbroken right now", she said.
MSG confirmed Monday's gig and said original tickets for Saturday's show will be honored for the new show set to start at 8 p.m. "It is chaotic now on the West Side, certainly".
As nighttime falls, New York Governor Andrew Cuomo has assured the public that authorities hope power supply will be restored by midnight.
More than 73,000 homes and businesses lost power in the blackout, officials said.
Power went out at Rockefeller Centre, reaching the Upper West Side. Several cast members from the show put on an impromptu performance in the street outside the theater for disappointed audience members. The lights of Radio City Music Hall were dark.
When the lights went out early Saturday evening, thousands of people streamed out of darkened Manhattan buildings, crowding Broadway next to bumper-to-bumper traffic amid emergency vehicle sirens and honking auto horns.
People spilled out into the streets as lights suddenly dimmed at Broadway shows and speakers fell silent at Jennifer Lopez's concert.
The blackout hit 42 years to the day after the massive 1977 power outage that wiped out electricity across almost all of the city.
The power outage comes on the 42nd anniversary of the 1977 Blackout which plunged most of New York City into two days of darkness.
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Officials say more than 40,000 customers were without power following a transformer fire in New York City.
"You just can't have a power outage of this magnitude in this city", Cuomo said Saturday.
Memories of the violence during the 1977 blackout spooked some tourists visiting the city, including Dave and Dara Campbell, of Gilbert, Arizona.
NYPD Commissioner James O'Neill said 400 police officers were dispatched to deal with the outage.
Con Edison engineers and planners are looking into what happened at a substation on Saturday evening that caused the blackout, which stretched 30 blocks from Times Square to the Upper West Side for about four hours.
The MTA did a truly heroic job in getting trains stuck in tunnels to the next station so that people could clamber upstairs, but the power cut in Midtown meant that a dozen lines - traveling from Brooklyn to The Bronx - were paralyzed.
The outage stymied subway service throughout the city, affecting almost every line.
New York City Mayor Bill de Blasio, campaigning in Iowa, tweeted the power outage was due to a manhole fire.
Con Edison is launching a full investigation into what caused the outage.
With some stations and traffic lights dark, many residents and visitors alike took to the streets and walked, according to social media posts, many of which had the hashtag #blackoutnyc.
"We were stuck for about 75 minutes", said O'Malley, 57.
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