An elderly woman has a sample for the Covid-19 at a swab collection site in Beijing on Monday. AFP

China is already trying to contain a wave of infections in its largest city Shanghai, which has been almost entirely locked down for weeks and reported 51 new Covid deaths on Monday.

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Shanghai has struggled to provide fresh food to those confined at home, while patients have reported trouble accessing non-Covid medical care -- and the rising cases in the capital triggered fears of a similar lockdown.

People wait in line to be tested for the Covid-19 at a swab collection site in Beijing on Monday. AFP

Downtown Beijing's most populous district Chaoyang, home to around 3.5 million people, ordered mass testing from Monday for residents and those coming to work there. The area hosts the headquarters of many multinational firms and embassies.

Queues snaked around malls and outside office complexes on Monday as people waited to be swabbed for samples by health workers in protective gear.

"If a single case is found, this area could be affected," said office worker Yao Leiming, 25, as he headed for a testing site in Chaoyang with a group of his colleagues.

A shopper leaves a supermarket with provisions as others wait in line to buy food supplies in Beijing on Monday. AFP

The mass testing order, and warnings of a "grim" Covid situation in the city, sparked a run on Beijing's supermarkets overnight as residents rushed to stockpile essentials.

Many items on grocery delivery apps sold out briefly on Sunday night after the testing order was announced, but stocks were replenished on Monday.

Beijing resident Zhao picked up several bags of groceries including eggs and fresh vegetables from a grocery store on Monday after hearing about the mass testing order.

The 31-year-old said he wanted to make sure his toddler would have enough to eat if the family was ordered to stay home.

People leave a supermarket after buying food and household provisions in Beijing on Monday. AFP

"Adults can survive for a few days, but it's not the same for children," Zhao, who only wanted to be known by his surname, told AFP.

Wang, another supermarket customer, said she was worried "things will become like in Shanghai".

"People are anxious... everyone is snapping up goods and we're worried that items might run out," the 48-year-old Chaoyang resident said.

Her family had secured enough food to last a week, she added.

Agence France-Presse