City authorities have repeatedly dismissed talk of broader curbs, even as they warned about risks posed by the highly-transmissible Omicron BA.5.2.1 subvariant.
All the 55 new local cases reported for Jul 12 were discovered among people already under isolation orders.
But many residents are stocking up on basic supplies, preparing for the worst.
“There are no signs that they will lock down our neighbourhood right now. But there were also no signs the first time,” said Omri Hephner, an Israeli business consultant.
“I will escape Shanghai as soon as I can this time, regardless of the signs I see,” Hephner said, adding that he intends to go to Beijing, then home to Israel, and will only return to China once COVID-19 policies are relaxed.
Overall, mainland China reported 261 new domestically-transmitted coronavirus infections on Jul 12, versus 347 the previous day.
Nomura analysts estimate more than 30 cities are facing COVID-19 curbs.
In the northwestern province of Gansu, which reported 69 local cases on Jul 12, the city of Lanzhou with over 4 million residents said on Wednesday that for the next seven days, only one person per household can leave residential compounds to get groceries. Non-essential workers are banned from going to offices.
In the central province of Henan, key urban areas in the city of Zhumadian entered a three-day lockdown from Tuesday, with residents only allowed out for COVID-19 tests, hospital visits and shopping for basic necessities.
The rules came after the town of Qinyang, which is under Zhumadian’s jurisdiction, imposed an indefinite lockdown from Sunday on its nearly 700,000 residents.
Infections have also been detected in the southern province of Guangdong, the eastern provinces of Shandong and Jiangsu and elsewhere.