Chinese residents are required to have the app, which displays a code indicating their health status, including possible exposure to COVID-19.
A green code is required to use public transport and to enter offices, restaurants and shopping malls.
But some depositors at the banks in central Henan province said their codes were deliberately turned red to stop them.
The incident has started a national debate on how a tool designed for public health was appropriated by political forces to tamp down controversy.
The issue started in April, when customers found they could not access online banking services. They tried to report the banks and get their money back, but did not get replies.
Thousands who had opened accounts with the six rural banks in Henan and Anhui provinces began trying to withdraw their savings after media reports that the head of the banks' parent company was on the run.
The majority shareholder of several of the banks, Sun Zhenfu, was wanted by authorities for "serious financial crimes", according to official media outlet The Paper.
Unable to resolve the issue online, customers set out earlier this week to demand government action at the Henan province office of the China Banking and Insurance Regulatory Commission in the provincial capital, Zhengzhou.
But after arriving in the city, they found they could not go far.
In one since-deleted account on the social media app WeChat, a woman surnamed Ai said shortly after she checked into a hotel in Zhengzhou, she was questioned by a group of police who asked her why she was there.
She replied that she wished to withdraw money from the bank.
Shortly after, she found her health code had turned red even though she had a negative COVID-19 test result in the previous 48 hours. She was immediately taken to a quarantine hotel.
Sixth Tone, a sister publication of The Paper, interviewed more than a dozen people who said their health app turned red after they scanned a QR code in the city.
When people are deemed to be at risk of COVID-19, their health code can be turned a different colour to indicate restrictions such as mandatory quarantine.
With a red health code, it is impossible to go to any public venue, or to board a bus or train.
One bank customer, who gave her last name as Liu, said she saw many people reporting their health codes had turned red after arriving in Zhengzhou.
Liu said she tested the code change after others reported it in a group chat.
After scanning the QR code from a photo shared in the group, Liu said her health code also turned red.
Another bank customer told Sixth Tone he got a red code after scanning in at the train station in Zhengzhou and was taken into police custody.
A few hours after police officers made him leave Zhengzhou, his health code turned green.
Jiakedao, a social media account run by the main Communist Party newspaper, criticised the Henan authorities in an editorial.
"Let's be frank, no matter which department or individual instigated it, arbitrarily using the epidemic prevention and control measures for 'social governance' or 'stability maintenance' should be strictly held accountable," the editorial said.
An official with Henan's Pandemic Control Committee said in response to Jiakedao authorities were investigating the reports of health codes being turned red.
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