The people, 761 in Da Nang and 120 in the neighboring Quang Nam Province came in contact with "Patient 416" and "Patient 418," both Da Nang residents.
All those tested have been placed in 14-day mandatory quarantine, some at home and others at specialized camps and hospitals.
Fifty more patients are awaiting their test results in Quang Nam.
Da Nang’s health sector has conducted continual epidemiological investigations into and quarantined those who had contacted the two confirmed patients.
"Patient 416", a 57-year-old man, became Vietnam's first Covid-19 community transmission in 100 days Saturday.
Treated at Da Nang Hospital, the patient is currently on ventilators and a extracorporeal membrane oxygenation (ECMO) machine, attended by doctors from HCMC's Cho Ray Hospital, who treated Vietnam's first Covid-19 patients as well as its most critically ill case - the British pilot.
"Patient 418" is a 61-year-old man who was confirmed infected Sunday morning, the second case of Covid-19 community transmission since April 16.
In critical condition, he is also being treated at Da Nang Hospital and is reliant on ventilator support, the Health Ministry stated.
Vietnam confirmed four local infections of Covid-19 over the weekend, including another case in Da Nang and one from the nearby Quang Ngai Province who had visited Da Nang recently.
The government ordered social distancing across Da Nang Monday.
The city plans to test a further 10,000 residents. It has banned entry for visitors and closed "non-essential" services like amusement parks, beauty salons, karaoke and massage parlors, and bars from Sunday afternoon.
In the wake of renewed local Covid-19 transmission, Vietnam has returned to pandemic prevention protocols on aircraft, trains, ships, and buses.
The Ministry of Transport on Sunday instructed all transport operators to install hand sanitizers, ensure everyone, including staff, wear masks at stations and in vehicles, and conduct temperature checks.
All passengers on long-distance journeys must complete health declaration procedures.
Such protocols were made mandatory in March when community transmission peaked.
Since April 16, the country had gone 99 days without a single local case of infection, until "Patient 416" was confirmed.
Authorities are still searching for the source of infection.
Of Vietnam’s 420 Covid-19 cases to date, 55 are still in hospital while the rest have recovered.