It comes as New York's virus-related deaths hit a record low - despite other U.S. states reporting surges in cases and outbreaks in Brazil and India hit landmark new levels. The district is in a "wartime emergency mode", he added.
The authorities plan to test more than 10,000 people working at the market for the virus.
Authorities are particularly alert to cases around markets because that is how the coronavirus spread: it emanated out from the Huanan food market in the city of Wuhan, across China and soon across the entire globe.
He has ordered 11 residential compounds around the market to be put under quarantine.
Officials said at a news briefing yesterday that six cases were reported on Friday, all related to the market, which sells meat, seafood, fruit and vegetables.
Tests at the market then showed 45 people had the virus.
School reopenings for first through third graders, planned for Monday, have also been delayed. One of the employees had visited the market last week.
"Preliminary judgement suggests these cases may have come into contact with a contaminated environment in the market, or were infected after being in contact with infected people", Pang Xinghuo, an official at the Beijing Center for Disease Control said.
The other two domestic infections reported Sunday were in northeastern Liaoning province, and local health officials said they were close contacts of the Beijing cases.
But last Thursday, a 52-year-old man became the city's first confirmed Covid-19 case in 56 days. He had shopped at Xinfadi market on June 3 and later developed a fever.
They also uncovered a further 45 asymptomatic cases in people associated with the market, and one linked to another market in neighboring Haidian district.
Workers will disinfect the market, while at least three other temporary markets have been set up to ensure supply is not disrupted.
The head of the Korea Centers for Disease Control and Prevention has pleaded with residents to stay home over the weekend, saying there was "high concern" that increased public activity would lead to a massive circulation of the virus. All sporting events have also been halted. Guards blocked shoppers from entering a popular shopping mall Saturday afternoon, insisting that they display green QR codes proving their health status.
By the end of Friday, Beijing authorities swabbed over 1,900 market workers in major supermarkets and food markets in the capital city, and had collected over 5,400 environmental samples.