The 70-year-old man was from the central city of Hoi An, state media said on Friday.
No new infections had been reported for more than three months before an outbreak was reported in the nearby resort of Da Nang earlier this week.
Vietnam, which has a population of around 95 million, has reported just 509 cases since the pandemic began.
Unlike many other countries, Vietnam acted before it even had confirmed cases, closing its borders early to almost all travellers, except returning citizens. Anyone entering the country must quarantine in government facilities for 14 days and undergo testing.
And for a while, this approach appeared to be highly effective, with no new local transmissions reported since mid-April.
The country received praise for both its timely efforts to contain the virus and for the care it was able to offer a Scottish pilot who spent two months in a coma after developing Covid-19..
But earlier this week came the difficult news that new cases had been discovered in the popular resort of Da Nang.
Tens of thousands of tourists from across the country were in the city at the time, many of whom believed the threat from coronavirus had passed.
The government initially closed the city to visitors, before ordering a total local lockdown on Wednesday.
Earlier this week, Prime Minister Nguyen Xuan Phuc warned that every province and city in the country following the outbreak in Da Nang.
“We have to act more swiftly and more fiercely in order to control the outbreak,” state media quoted him as saying.
What this means for Vietnam
By Bui Thu, BBC News Vietnamese
At first, Vietnamese mainstream newspapers cited coronavirus as the main cause of the man’s death. But then, just a moment later, the story was deleted from most of the country’s state media websites.
The story only appeared again on their websites as the National Steering Committee for COVID-19 Prevention and Control finally confirmed the news.
Talking to the BBC Vietnamese Service, Dr Luong Ngoc Khue, vice-director of the Treatment Subcommittee under the National Covid-19 Taskforce, said the person “died of heart attack, kidney cancer, high blood pressure and other severe diseases while positive for coronavirus”.
Some speculate that the government found it difficult to announce the first death for fear of public embarrassment.
But as the news was confirmed today, Vietnam is trying to carry out an aggressive prevention strategy to contain the virus, with many quarantine facilities and mobilising all means and resources to treat every patient.
Since July 25, 93 cases linked to Da Nang have been reported, and now the city is under a lockdown again. Restrictions are also being reintroduced in many other cities and provinces.