The bus was travelling from Samara on the Volga river to Izhevsk, around 900 kilometres (550 miles) east of Moscow, when the accident happened, according to the Investigative Committee, which probes major crimes.
The committee said it was possible the bus driver was blinded by headlights.
The bus rolled over and caught on fire as a result of the collision, the regional interior ministry said, adding that it would be arresting both drivers.
The committee said it has already detained the director of a passenger transport company and searched the firm's premises, although it was not clear how the company could have been involved in the crash.
Another deadly accident occurred in southern Russia, where a passenger car span out of control and collided with a tree and a parked vehicle, killing five people inside, the regional traffic police force was cited by Interfax agency as saying.
Russia ranks among the world's worst countries for road deaths, mainly due to drink-driving, poor roads and traffic violations.
Last year more than 20,000 people died in road accidents, a 12-percent drop from 2015.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)