The bus was travelling from Samara on the Volga river to Izhevsk, around 900 kilometres (550 miles) east of Moscow, when the accident happened, the Investigative Committee, which probes accidents and disasters, said.
It 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 it would be arresting both drivers.
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 compared to 2015.
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