Many said they have been confined to their quarters for days and that distribution of food and other essentials has been chaotic. Many others say they are too scared to carry on working because of the risk of getting infected.

Foxconn on Wednesday denied what it said were online rumors that 20,000 cases had been detected at the site and said that for “the small number of employees affected by the pandemic,” it is providing necessary supplies.

“A sudden outbreak disrupted our normal life,” Foxconn said Friday in a post to its workers on

WeChat,

a social-media platform. “An orderly progress in both pandemic prevention and output depends on the efforts of all staff,” it said. It outlined plans to ensure proper food supplies and mental well-being support and pledged to respond to workers’ concerns.

Asked about the workers’ details of the situation at the site, Foxconn didn’t respond. Earlier when asked about the situation, the company referred to its Wednesday statement as well as to its Friday post on WeChat.

“It’s too dangerous to go to work,” a 21-year-old worker who has been confined to his dorm told The Wall Street Journal, saying that he was skeptical about the company’s claim that there was a low level of infections at the plant.

The disruption at Foxconn is the latest example of the economic and societal toll from China’s rigid pandemic control policies—which include swift and sweeping lockdowns, mass testing and compulsory quarantines to crush the virus whenever it appears. While Beijing says the virus is too potent to allow any easing of its zero-Covid policy, businesses must convince their employees that there is little risk coming to work when there are signs of an outbreak.

Zhengzhou’s flare-up—95 cases recorded in the city the past four days—began in early October, after people returned from other parts of the country from a one-week national holiday. At the first signs of Covid in the city, officials locked down some districts and began rounds of mass testing to stamp out the virus before it gained a foothold among Zhengzhou’s 12.7 million residents. As a major employer, Foxconn joined the campaign.

When more infections emerged at Foxconn midmonth, the company sought to maintain output by creating a “bubble” around its operations to lower the risk of exposure, a practice now common among major manufacturers in China to continue their business during a local outbreak.

Foxconn says it employs as many as 300,000 workers in Zhengzhou. Analysts estimate that the company produces half or more of Apple’s smartphones in the city, making it vital for delivering iPhones to consumers, including for the coming winter holiday season when demand for the handsets typically spikes.

Foxconn, in its statement on Wednesday, said that production at the site is “relatively stable” and that it is sticking to its operating outlook for the current quarter as the impact from the outbreak is controllable. It is set to report quarterly results Nov. 10.

Apple, in its quarterly earnings release Thursday, didn’t mention Foxconn’s Zhengzhou plant. Its chief financial officer said that supply is constrained for the new iPhone 14 Pro models due to strong demand.

Apple didn’t respond to requests for comment about conditions at the Foxconn plant.

Some workers interviewed by the Journal said many colleagues had refused to go back to the production lines. Others had simply left, they said, sometimes abandoning their belongings.

On Sunday, a state-run newspaper in Henan published official notices from various parts of the province welcoming their people to return, with quarantine protocols laid out.

Over the weekend, videos geotagged near the Foxconn site went viral on China’s social-media platforms, recording groups of people walking on highways or through farm fields carrying suitcases and backpacks. Other footage showed makeshift stations set up by local residents offering bottles of water in front of handwritten signs to support migrant Foxconn workers leaving for home.

Foxconn said in a statement Sunday that the situation is coming under control with help from authorities. The company said it is organizing transportation for workers who wish to return home and is coordinating production capacity with its plants elsewhere to minimize disruption. There is no shortage of medical supplies or daily necessities at the facility, it said.

Earlier on Friday, the company had posted a video on WeChat urging people to return to work. “The company needs people,” said a woman’s voice over footage of workers stepping off a bus. “If nobody comes to work, how can the company run?”

Another Foxconn employee said most of his dozen-strong team of night-shift workers had either been taken to a quarantine facility or had refused to return to work. Every night, he said, he saw workers covered in protective gear waiting to be taken away by bus.

“I don’t know who around me is a positive case,” said the worker, who has been confined to his dorm for a few days. “I’d be better off staying in the dorm.”

With so many stuck inside their quarters, sent to quarantine centers or simply absent from work, the pace of production at some assembly lines has slowed, two of the workers said.

Foxconn has created incentives to maintain production, according to Friday’s company notice.

Anyone turning up for work will get free meals and a daily bonus, it said. Those turning up every working day from Oct. 26 to Nov. 11 will get an award of 1,500 yuan, or about $200.

The 21-year-old employee who spoke to the Journal and who worked on an assembly line making an older iPhone version, said he had been confined to his quarters since Oct. 17, along with thousands of others.

Over the following days, meal deliveries were delayed and garbage was left unattended in the hallways, piling up on the ground floor as more dorms were locked down, he said.

A daughter of one worker said her mother was placed in the same dorm as some who tested positive. Some other workers made similar complaints.

Around 10 days ago, almost 300 employees from Foxconn suppliers were asked to move out of their dormitories and sleep in the factory, one of them said.

In photos he shared with the Journal, people slept on bedding and pillows placed on metal bed frames, under white fluorescent lights suspended from the hangar-like roof. Hygiene has become a problem, he said. Still, he said he isn’t supposed to leave the plant—and has nowhere to go if he did.

“Where can I go? Barriers are everywhere,” he said. “There are people manning every checkpoint.”

Write to Wenxin Fan at Wenxin.Fan@wsj.com and Selina Cheng at selina.cheng@wsj.com