Nguyen Ngoc Sang, 38, drove the Hanoi-bound bus with 30 passengers. At around 11:50 p.m., at an intersection in the provincial capital, also named Ninh Binh, the bus collided with a motorbike driven by 70-year-old Vu Minh Tam.
Tam, along with three bus passengers - Phan Uy Vu, 12, Nguyen Tat Nga, 20, and Nguyen Tai Thai, 20 - were killed as a result.
Nguyen Van Hanh, deputy director of the Ninh Binh Department of Transport, said 13 others were injured.
Ninh Binh police said the bus was not authorized to enter Ninh Binh Town.
They are investigating further.
Since Monday evening, Ninh Binh and several other northern Vietnam localities saw heavy rains due to the impact of a low-pressure system.