A woman set fire to a restaurant in Manhattan’s SoHo neighborhood early Monday by igniting a gay pride flag hanging on the business’s facade in an act of arson that was being investigated as a possible hate crime, the police said.

The fire, at Little Prince on Prince Street, occurred shortly after 1:35 a.m., the police said. Security-camera footage released publicly as part of the investigation shows a white SUV stopping in front of the restaurant and waiting while a woman gets out, approaches the building, pulls out a lighter and touches it to a rainbow-colored flag.

After igniting the flag, the woman hops back into the passenger side of the vehicle, which drives west on Prince Street, the police said. The restaurant was closed at the time, and no one was injured in the fire, the police said. It caused minor damage to the facade and none to the interior.

Twelve Fire Department units and 60 firefighters and emergency medical responders were involved in extinguishing the fire, officials said. Fire marshals were investigating, officials said.

The Police Department’s Hate Crime Task Force was also investigating, according to officials, who asked for the public’s help in identifying the woman who started the fire. She is clearly visible in the security footage.

Later in the morning, City Councilman Erik Bottcher of Manhattan arrived at the restaurant to hang a larger rainbow flag out front as television news cameras captured the scene.

“The person who did this, their plan has backfired and backfired badly,” Mr. Bottcher said.

By midafternoon, workers were busy inside and outside the restaurant, painting, moving chairs and tables and replacing windows. The charred remnants of an outdoor dining shed sat on the sidewalk; half of a decorative banner of flowers above the facade was missing.

Little Prince is operated by Prince Hospitality Group, which is led by Cobi Levy and Will Makris. The company’s other restaurants include Lola Taverna and Alba in Manhattan and Lucali in Brooklyn.

Mr. Levy was at Little Prince Monday afternoon as workers prepared to open for dinner service at 5 p.m. People stopped by to express their shock at what had happened and their support for the restaurant. He declined to comment to a reporter.

A neighbor, Al DiRaffaele, 77, called the fire “a horrendous act.”

“Picking on a flag, you know, there’s no reason for that,” he said.

Explaining that he was gay and a Vietnam War veteran, Mr. DiRaffaele said, “This is war here in America against the L.G.B.T. group.”

“It affects me, being a gay man,” he said. “It’s a slap in my face, along with every gay person in the world.”

Little Prince is at least the second restaurant on Prince Street to be targeted by an arsonist in recent years.

In 2021, a highly regarded sommelier was charged with setting several fires in Lower Manhattan, including one that damaged a dining shed at Prince Street Pizza and another that destroyed a similar structure at the restaurant Forsythia.

The sommelier, Caleb Ganzer, later reached an agreement with the Manhattan district attorney’s office that called for him to pay the owners of the two restaurants thousands of dollars to cover the cost of the damage he had caused.

At Little Prince, Mr. Levy appeared pleased as workers closed in on finishing the repairs that would allow the restaurant to open, with the replacement flag hung overhead.

“Now it is getting there,” he was overheard saying. “Now we’re back.”

Brittany Kriegstein contributed reporting.