Gov. Andrew M. Cuomo of New York announced on Wednesday that baseball fans who have been fully vaccinated against the coronavirus will soon be able to enjoy seating arrangements without social distancing at Yankee Stadium and Citi Field, and that spectators who get vaccinated at either stadium during a game will get a free ticket.

Beginning on May 19, the same day the state is ending most capacity restrictions for businesses, fully vaccinated people will be allowed to sit in sections of the stadiums where every seat can be occupied, though they will have to wear masks. They can also be accompanied by children who are under 16 and unvaccinated, who must also wear masks.

People who have not been vaccinated will sit in sections where only one-third of the seats can be occupied, and will have to observe six-foot social distancing rules. Both Yankee Stadium and Citi Field, the home of the Mets, are mass vaccination sites, and both stadiums will offer a voucher for a free ticket to people who are vaccinated there on game days, as an incentive to receive the vaccine.

You take a vaccine shot, get a voucher, you can go to that game, Randy Levine, the president of the New York Yankees, said at Mr. Cuomos news conference. If that games sold out, you can go tomorrow night, go to a game of your choice.

The Johnson & Johnson vaccine, which only requires one shot, will be offered to game attendees, the governor said, so they will not have to schedule a follow-up appointment.

Social distancing, capacity rules and other safety measures vary significantly from one Major League stadium to another, because of differing local regulations and individual team decisions.

Mr. Cuomo also announced that Broadway shows would start selling tickets on Thursday for full-capacity shows with performances starting Sept. 14.

Broadway, home to 41 theaters with between 600 and 1,900 seats, drew 14.6 million people who spent $1.758 billion on tickets in 2019. The pandemic had forced them all to close since March 12, 2020, and reopening is clearly going to be far more complicated than shutting down.

With as many as eight shows a week to fill, and the tourists who make up an important part of their customer base yet to return, producers need time to advertise and market. They need to reassemble and rehearse casts who have been out of work for more than a year. And they need to sort out and negotiate safety protocols.

But the biggest reason for the delay is more gut-based: Individually and collectively, they are trying to imagine when large numbers of people will be likely to feel comfortable traveling to Times Square, funneling through cramped lobbies and walking down narrow aisles to sit shoulder to shoulder with strangers. (Most Broadway shows lose money even in the best of times, so producers say there is no way they can afford to reopen with social distancing, given the industrys high labor and real estate costs.)

The governor said that the states coronavirus indicators were all trending downward, so reopening made sense, though the state would continue monitoring the situation carefully.

According to a New York Times database, the average number of new cases a day in the state had declined by 46 percent in the past 14 days, as of Tuesday. Thirty-seven percent of the states population was fully vaccinated, as of Wednesday.

The virus does appear to be ebbing in New York City. But the city still faces challenges from uneven vaccine coverage, the slowing pace of vaccinations and the growing prevalence of variants in the city.