New York City restaurants are being crushed by the US' current labor shortage - and it could take months for them to reach proper staffing levels, restaurateur Danny Meyer told CNBC's "Closing Bell" Wednesday.

"Nobody can hire back all of their workers even if they wanted to because many of our workers have left the city," Meyer said. He founded Shake Shack and is the CEO Union Square Hospitality Group, the parent company of New York City hotspots Union Square Cafe and Gramercy Tavern.

Many restaurant workers left NYC because they couldn't afford to live there without their usual wages during the pandemic, Meyer said. He added that many laid-off staff got jobs in other industries "that were actually doing quite well during COVID," and may not return to hospitality.

The fast-food industry is facing a crushing labor shortage, causing restaurant chains such as Subway and Dunkin' to cut opening hours and close dining rooms.

Chipotle, Taco Bell, and others are offering lucrative perks such as cash bonuses, raises, and education benefits to attract new staff. A McDonald's restaurant is even offering free iPhones to new hires.

"Everybody is hiring at the exact same time," Meyer, who also chairs the NYC Economic Development Corporation, said.

"It is going to take, in my judgement, at least two or three months for supply and demand to keep up with each other and to hit an equilibrium," he added. The scramble for workers comes after Union Square Hospitality Group laid off 2,000 workers - or four in five staff - last March when the pandemic hit and New York banned dine-in services.