The company could now see more than 30% of the site's November production affected, up from an internal estimate of up to 30% when the factory's worker troubles started in late October, the source said.
The site, which is the only factory where Foxconn makes premium iPhone models, including the iPhone 14 Pro, is unlikely to resume full production by the end of this month, the source added.
The world's largest Apple iPhone factory has been grappling with strict COVID-19 restrictions that have fuelled discontent among workers and disrupted production ahead of Christmas and January's Lunar New Year holiday, as many workers were either put into isolation or fled the plant.
It has fuelled concerns over Apple's ability to deliver products for the busy holiday period, as the Zhengzhou plant accounts for 70% of global iPhone shipments and produces the U.S. company's popular iPhone 14 models.
On Wednesday workers, most of whom were new recruits hired in recent weeks, clashed with security personnel.
Many claimed they were misled over compensation benefits at the factory, and others complained about sharing dormitories with colleagues who had tested positive for Covid.
Foxconn apologised for a pay-related "technical error" when hiring on Thursday, and later offered 10,000 yuan ($1,400) to protesting new recruits who agreed to resign and leave.
The source said more than 20,000 workers, mostly new hires not yet working on production lines, took the money and left. Videos posted on Chinese social media on Friday showed crowds and long lines of luggage-laden workers queuing for buses.
"It's time to go home," one person posted.
Foxconn, formally known as Hon Hai Precision Industry Co, declined to comment. Apple, which said on Thursday it had staff at the factory, did not immediately respond to a request for comment on Friday.
The plant, before its woes began, employed more than 200,000 staff. It has dormitories, restaurants, basketball courts and a football pitch across its sprawling roughly 1.4 million-square-metre (15 million-square-foot) facility.
Another Foxconn source familiar with the matter said some new hires had left the campus but did not elaborate on how many. This person said that because the people leaving had not yet been trained or begun to work, their departures would not cause further harm to current production.
"The incident has a big impact on our public image but little on our (current) capacity. Our current capacity is not affected," the source said.
"There's only so much corporate can do on pandemic prevention ... It's been a problem for a while. This is a problem faced by everyone," the person said, pointing to other worker unrest triggered by rigid COVID restrictions, including upheaval at another Apple supplier, Quanta, in May.
Foxconn shares closed down 0.5%, lagging the broader market, which ended flat.