The eastern city's health commission said the victims were aged between 89 and 91 and unvaccinated.
They “deteriorated into severe cases after going into hospital and died after all efforts to revive them proved ineffective”, the city said on an official social media account.
All three had underlying health conditions, it said.
The municipal health commission confirmed the deaths.
Shanghai officials said only 38 per cent of residents over 60 are fully vaccinated.
Since the discovery of an Omicron-led outbreak three weeks ago, the city has been under strict lockdown. This has led to rare protests by residents.
Restriction orders have kept most of Shanghai's 25 million residents confined to their homes or residential compounds, with daily caseloads edging over 25,000.
The city has converted exhibition halls and schools into quarantine centres and set up makeshift hospitals.
Many residents have complained of food shortages, basic quarantine conditions and heavy-handed enforcement.
Residents have had to order food and water and wait for government drop-offs of supplies. Analysts have said many are running low on basics.
The lockdown extension has overwhelmed delivery services, grocery shop websites and even the distribution of government supplies.
Shanghai reported 22,248 new domestic cases on Monday, according to the municipal health commission.
China has recently struggled to contain outbreaks in multiple regions, largely driven by the fast-spreading Omicron variant.
The country last reported Covid-19 deaths on March 19 — two people in the north-eastern province of Jilin. Those were China's first confirmed coronavirus deaths in more than a year.
Agencies have contributed to his report.