"Tomorrow we need to intensify inspections, and any case not in a category of those allowed to go outside will be fined," Chung said at a Friday meeting of the city's Steering Committee on the Prevention and Control of Covid-19.
He did not elaborate on how the authorities would determine if someone was out for non-essential reasons.
Chung repeated his call for everyone to stay at home as the capital city is entering a new phase in which the Covid-19 virus could spread easily in the community. He stressed that the city needs to implement "heavy" measures in order to prevent Covid-19 from spreading in the community.
Over the past week, Hanoi has constantly been detecting new Covid-19 cases, with the number of cases reaching nearly twice that of three weeks earlier.
Since Wednesday, Hanoi has been implementing a 15-day social distancing campaign, asking people not to venture outside their homes except for essential reasons like buying foods and medicine or other emergencies.
Those working at establishments that produce or provide essential goods and services are allowed to go outside.
Citing experts' analysis, Chung claimed that "wrongdoing by 10 percent of the population (by increasing the frequency of going outside) could raise the infection rate from 30 percent to approximately 60 percent of the population."
"If the wrongdoing is committed by 40 percent of the population, the distancing will make no difference and have no value," he said, reiterating that people staying at home was a vital solution to preventing the spread of the disease.
Chung's order to fine those going outside for non-essential reasons was issued after many Hanoians were found gathering in large groups in public places despite the social distancing campaign.
Many people were found exercising in public parks and some internet cafés still operating in secret. Tay Ho District was criticized for allowing people to gather in large crowds for religious activities earlier.
Hanoi has recorded 107 Covid-19 cases as of Saturday noon. Of these, 36 were traveling from infected areas and tested positive at the airport or under centralized quarantine facilities.
Following the discovery of a Covid-19 outbreak at Bach Mai Hospital, which is now linked to 44 cases, Hanoi's health authorities have verified over 22,500 cases of suspected infection in the community and conducted tests on more than 4,700 people. A total of over 1,800 cases have tested negative for the novel coronavirus and four have tested positive, while the remaining cases are awaiting test results.
Hanoi has purchased 105 ventilators in addition to the 236 units the city already had prior to the outbreak and is planning to purchase another 37 units. The city has also bought 300,000 sets of protective clothing and is planning to buy another 770,000 sets.
Vietnam has recorded 239 Covid-19 cases so far, of whom 86 have recovered and been discharged from hospital.
Globally, the Covid-19 pandemic has claimed more than 59,000 lives as it spread to 205 countries and territories.