The Jitiya festival lasts for several days and is also celebrated in the neighbouring states of Uttar Pradesh and Jharkhand and the southern plains of Nepal.
The government official said that the Bihar government has announced compensation for every affected family.
Last year, local media reported that 22 people drowned in a 24-hour period in Bihar, most of them while celebrating a single festival.
Fatal incidents at places of worship are common during major religious festivals in India, the biggest of which draw millions of devotees to pilgrimages to holy sites.
In July, at least 116 people were crushed to death at a crowded Hindu religious gathering in Uttar Pradesh, the worst tragedy in more than a decade.
Every year in India, the monsoon season from June to September brings torrential rains and floods.