A Covid-19 testing firm in Shanghai is being investigated by city officials after reports that residents were given false-positive results that landed them in harsh state quarantine.

The city has been under lockdown for weeks as China enforces a zero-Covid policy through shutdowns, mass testing and tight restrictions on movement -- with everyone who tests positive being sent to a government isolation centre, even those without symptoms.

Numerous Shanghai residents wrote on the Twitter-like Weibo platform this week that they received false-positive results from Zhongke Runda, which operates three testing centres in the financial hub of 25 million.

The group's parent company, Shanghai Runda Medical Technology, said in a stock filing Wednesday that reports about false positives have "casts doubt on the accuracy of Zhongke Runda's lab nucleic acid testing data" and an investigation is being held. 

The group's shares have slid since the reports first started on Monday.

Shanghai health authorities said they had declared an investigation into an unspecified "third-party testing organisation" in response to online comments about test results.

One woman said her daughter got a positive result after a Runda test and was sent to a quarantine facility with bad conditions.

"On May 7, my exam-prepping daughter who has barely left the house tested false positive," the Weibo user wrote. 

Her whole family were "thrown into a scary-looking quarantine centre" where the lights were on 24 hours a day and there was no medical care, she said.

Residents who test positive face extended stays in crowded facilities. In some cases, entire buildings are sent into quarantine if one resident tests positive.

Another resident, who initially received a false-positive test from Runda, said they later tested positive after spending four days in quarantine.

As fears mount a lockdown may be imposed in the capital, Beijing officials on Monday said that they were investigating issues with an unspecified number of testing institutions, including inaccuracies.

At least 15 major cities across China now require residents to get Covid-19 tests every two to seven days, according to research firm Soochow Securities.

Nomura economists estimate that regular mass testing could cost as much as 1.8 per cent of China's GDP.