New York City diners have seen their social media feeds flooded in recent days with announcements from restaurant after restaurant that they were temporarily closing because staff members tested positive for Covid-19 or were exposed to the virus.

“I feel like it happened in three days,” said Cat Alexander, who on Wednesday closed Pheasant, her restaurant in Williamsburg, Brooklyn, after an employee received a positive test result. She is waiting for her remaining 22 employees to test negative before reopening.

At least a dozen restaurants and bars have temporarily closed this week, as the reported number of new Covid cases in New York City has risen to an average of 3,554 a day in New York City, an increase of 135 percent from the average two weeks ago, according to a New York Times database.

Restaurateurs said the cases reported so far had been mild, but they expected the number of shutdowns to grow as businesses try to shield employees and customers from infection. The restaurants include Contento in Harlem, Temperance Wine Bar in the West Village and several in Brooklyn: Otway in Clinton Hill, LaLou in Prospect Heights, Winona’s in Bedford-Stuyvesant, Di An Di in Greenpoint.

“It was pretty unbelievable and shocking to me, the rate of how much it could spread within such a safe environment,” said Jamie Erickson, the owner of Poppy’s, a cafe in Cobble Hill, Brooklyn. Her staff of 30 is vaccinated and always masked on the job, but the cafe’s commissary kitchen in Red Hook closed during the weekend after Thanksgiving because of a Covid outbreak.

Across the country, coronavirus cases have prompted similar shutdowns as both the Delta and Omicron variants advance. There have been restaurant closings in Massachusetts, Maryland, Virginia. New Mexico, Oregon, Hawaii and other states.

The New York City closings, like those now occurring at several Broadway shows, come in the thick of the holiday season, normally one of the busiest times of the year for those businesses.

Just as they were over the summer, when the Delta variant became the most predominant strain of the coronavirus in the United States, restaurant owners have been forced once again to reassess their safety protocols, and feel inadequately supported by local and state governments.

New York City has some of the most stringent vaccine requirements in the country, requiring that workers and indoor diners provide proof of vaccination. On Monday, Gov. Kathy Hochul ordered all indoor businesses in the state to require that customers wear masks, unless the businesses have protocols for demanding proof of vaccination.

Many restaurants are going beyond the official requirements — at Pheasant, the entire staff is not only fully vaccinated (several employees have received booster shots), but must also wear masks. Ms. Alexander hopes she can reopen on Thursday night, but she is at the mercy of the testing centers’ speed in providing results. Many testing centers are experiencing long lines and delays.

As Covid caseloads rise, the question for many restaurant owners is how to manage their exposure while keeping their businesses afloat.

On Wednesday, an employee at Di An Di, a Vietnamese restaurant in Greenpoint, tested positive for the virus. Dennis Ngo, an owner, said he wanted to reopen as soon as workers received a negative result from a PCR test or two consecutive rapid tests. He said some of the nearby testing centers he visited on Wednesday had run out of rapid tests.

“I am very surprised,” Mr. Ngo said. “I thought we had gotten over this testing hump.”

He said that although all 30 of his employees were vaccinated, and any Covid cases were not likely to put them in the hospital, they would be losing income at a crucial time of buying gifts and paying bills. The restaurant could also lose significant revenue from big holiday dinners.

Mr. Ngo is thinking about reintroducing delivery and takeout, in case he has to shut down indoor dining again. “I foolishly thought we had gotten past this,” he said.

Brent Young, who on Wednesday closed his restaurant Cozy Royale, in East Williamsburg, Brooklyn, said he had received “zero guidance” from city and state officials about what to do when an employee tests positive for Covid.

“Even the C.D.C. website says, if you don’t have any symptoms, just go about your life as normal,” he said, referring to the Centers for Disease Control and Prevention. “So I think we are going above that recommendation by getting everyone to isolate and take a test.”

The sudden increase in the city’s coronavirus numbers is likely due to the Delta variant and the growing number of indoor gatherings for the holidays, said Dr. Larry Brilliant, a California-based epidemiologist who was part of the effort to eradicate smallpox in the 1970s. The Omicron variant is still fairly new, he said, but it is the most transmissible of any existing variant.

The Northeast, especially New York City, has been a popular entry point for the virus and its variants because of tourism, said Bill Hanage, an associate professor of epidemiology at Harvard University. “Where New York City is going is where we expect the rest of the country to be,” he said.

The loss of revenue from closing just before Christmas is especially sharp at many restaurants. Because an employee tested positive on Tuesday, Contento, in Harlem, will be closed at least through Saturday. This has meant canceling a large private event, and sitting out one of the most lucrative weeks of the year, said Yannick Benjamin, Contento’s sommelier. (This week, the restaurant was ranked No. 4 on the New York Times critic Pete Wells’s list of the year’s 10 best new restaurants in the city.)

Mr. Benjamin said the restaurant keeps Covid tests on hand for employees; all are vaccinated and many have gotten a booster shot.

“I can’t imagine how much more rigid we can be” with employees, he said. It’s hard to control their actions when so much of the city is open for business. No matter how diligent people are, he said, “things happen.”

At the Clinton Hill cafe Otway, there are two separate staffs for daytime and nighttime, so that if someone from one team tests positive, the other team can still work, and an entire day of business is not lost. On Tuesday, an employee reported having been exposed to Covid-19, so the owner, Samantha Safer, shut down dinner service the following evening. She estimated she lost $4,000 to $8,000 in that one night.

What is especially frightening to her is that, as safe as her employees are being, some guests are not extending the same courtesy. She said a server overheard three indoor diners “who were talking about how they might have been exposed to Covid.”

Ms. Safer isn’t taking any chances this New Year’s Eve, typically the restaurant’s highest-grossing night. In addition to showing their proof of vaccination, she said, diners will have to produce a negative result from a recent test.