The storm, which claimed 13 lives in the Philippines over the weekend, tore through the communist country's central region from the tourist town of Hue to Quang Ngai to the south, Vietnam Television reported.
Trees were uprooted and thousands of houses had their roofs ripped off while many roads became impassable due to torrential rain, footage showed.
Schools were closed today in Danang city, which bore the brunt of the typhoon when it hit packing winds of up to 133 kilometers an hour, state media said.
Before Nari hit, Vietnam evacuated more than 1,20,000 people to makeshift shelters in public buildings away from vulnerable coastal areas, according to the country's disaster authorities.
Vietnamese weather forecasters said the typhoon had crossed the border to Laos by today. Nari is the 11th tropical storm to hit Vietnam so far this year.
Last month Typhoon Wutip left a trail of destruction in the communist state, damaging nearly 2,00,000 houses and killing several people. Forty people have been killed in flooding in Vietnam since early September, according to official figures.