Hundreds of police have been deployed in the area
The violence erupted on Sunday in Ajitpur in Muzaffarpur district.
It came after the body of a Hindu man was found in the village more than a week after he went missing.
A senior police official told BBC Hindi the man had been in love with a Muslim girl. ?He was abducted and murdered,? he said.
?A mob gathered after the body was found and set fire to at least two dozen thatched huts and at least three people were killed,? Additional Director General of Police Gupteshwar Pandey said.
?The situation is tense but under control,? he added.
Officials said the young man?s father had lodged a missing person complaint with the police on 11 January, accusing a Muslim man of abducting his son.
The government of Bihar state has ordered an inquiry into the incident, and hundreds of police have been deployed.
Hindus comprise more than 80% and Muslims less than 14% of India?s 1.2 billion people. Correspondents say they largely live peacefully, but there is occasional violence.
In September last year, nearly 50 people died in Hindu-Muslim clashes in Muzaffarnagar town in the neighbouring state of Uttar Pradesh.