The city police department spelled out the restrictions that most of the 25 million residents are facing and called on them to "fight the epidemic with one heart ... and work together for an early victory".
"Those who violate the provisions of this notice will be dealt with in strict accordance with the law by public security organs ... If it constitutes a crime, they will be investigated according to law," the department said in a statement.
The financial hub is under huge pressure to try to contain China's biggest Covid-19 outbreak since the coronavirus was first discovered in the city of Wuhan, some 800 km (500 miles) to the west, in late 2019.
Shanghai police also warned increasingly frustrated residents, millions of whom are confined to their homes and struggling to get daily supplies, not to spread false information or forge road passes or other clearance certificates.
Residents battling to secure delivery slots for their food are also facing surging prices which the government is keen to keep a lid on.
Peng Wenhao, an official with Shanghai's market supervision bureau, told reporters that authorities had issued 38,000 letters of warning against price gouging and was also investigating complaints of irregular pricing on social media.
"If illegal acts like price gouging take place, it will be investigated and punished firmly and quickly," he said.
Police also banned cars from the streets except for those involved in epidemic prevention or transporting people in need of emergency medical treatment.
Shanghai reported 25,141 new asymptomatic coronavirus cases for Tuesday, up from 22,348 a day earlier, and symptomatic cases also jumped to 1,189 from 994, city authorities said.
Shanghai's Covid measures, which reflect China's strict "zero-Covid" approach aimed at eliminating transmission chains, have reverberated through the global economy, with analysts warning they were not only hurting tourism and hospitality but also having an impact on supply chains across sectors.
Imports last month fell for the first time since August 2020, data showed on Wednesday, with Covid curbs hampering freight arrivals and weakening demand.
"The widespread lockdown and tighter zero-Covid restrictions in several cities around Shanghai have caused significant supply disruptions with transport and logistics under severe pressures," Barclays Bank economist Jian Chang said in a note.
At least 11 Taiwanese companies, mostly making parts for electronics, said on Wednesday they ere suspending production because of the disruption from China's Covid controls.
Chang said the economic and supply pressures "likely have speeded up the transition towards a gradual and cautious exist from zero-Covid".
The Caixin media group reported that Shanghai was one of eight cities involved in a pilot scheme launched on Monday to lower centralised quarantine requirements from 14 to 10 days, citing a government plan set out in a document that has not been formally published.
Relevant authorities were not immediately available for comment on the report.