The seven-seater car, carrying eight people, was proceeding on National Highway 1A in the central province of Thanh Hoa, visiting relatives during the Tet holiday.
As it turned left into Quy Chu Village in Hoang Hoa District, the speeding bus slammed into it.
The car was dragged for around 20 meters with all passengers stuck inside, some of them pleading with local residents to break the door and take them to the hospital.
Three people succumbed to injuries the same day. Five others are still at the hospital in critical condition.
More information about the accident has not been released.
Deputy Prime Minister Truong Hoa Binh has ordered an urgent investigation into the accident and directed authorities to take follow-up measures.
Road crashes are a leading cause of deaths in Vietnam, killing almost one person every hour. A total of more than 18,720 traffic accidents occurred in 2018, killing 8,244 people and injuring nearly 14,800, according to the National Traffic Safety Committee.
During the nine-day Lunar New Year holiday starting February 2, the country recorded 214 traffic accidents that killed 135 people and injured 154 others.