The fire broke out on the non-nuclear side of the plant, about 200 yards away from the reactor building, according to Entergy spokesman Jerry Nappi.
"The fire is out and the plant is safe and stable," Nappi said. Federal officials said one reactor unit automatically shut down.
No one was injured in the blaze.
There was "no threat to public safety at any time," the facility said in a tweet. "All Indian Point emergency systems worked as designed."
A sprinkler system doused the fire with the help of personnel on the scene, Nappi said.
Multiple emergency services agencies responded to the explosion at the plant, located approximately 50 miles north of Manhattan, including the Westchester County and New York State Police.
"We saw just a huge black ball of smoke right across the river," witness Gustavus Gricius told CNN. "We could smell the oily, electric burn smell."
Gov. Andrew Cuomo was at the plant and received a briefing on the accident.
He called the incident "relatively minor" but added, "these situations we take very seriously. This is a nuclear-powered plant; it's nothing to be trifled with."
The blast sent the facility into an emergency response situation classified as an "unusual event," according to Nappi.
The event was declared at 5:50 p.m. and the fire was out by 6:15 p.m.
Neil Sheehan, a spokesman for the federal Nuclear Regulatory Commission, said the agency had three inspectors respond.
"They're cooling down the reactor and we'll have to investigate the cause of the fire," he said.
The facility houses two nuclear reactor units and produces approximately 25% of the electricity for New York City and Westchester County, according to its website.