The warning comes as some question the accuracy of the government's official figures of the number of those infected or dead from the virus.
"This year's Christmas eve, New Year's Day, and the Lunar New Year are destined to be unsafe," warned Shanghai Deji hospital in a statement.
"In this tragic battle, the entire Greater Shanghai will fall, and we will infect all the staff of the hospital! We will infect the whole family! Our patients will all be infected! We have no choice, and we cannot escape," it added.
The statement, shared on its official WeChat account, said about 5.43 million residents in Shanghai are already positive and another 12.5 million in China's main commercial hub will get infected by the end of the year.
The post was no longer available on WeChat by yesterday afternoon and the claims made by the hospital could not be verified independently.
Even though China did not report any Covid deaths for a second consecutive day on Wednesday, workers in funeral stations said demand for cremation services has shot up in the past week.
The official death toll in China since the pandemic began three years ago stands at 5,241, with authorities saying there are 389,306 cases with symptoms.
A British-based health data firm, Airfinity, which said it had examined data from China's regional provinces, suggested infections could be as high as more than a million a day, noting that cases are rising quickly in the capital Beijing and southern province Guangdong.
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