Curfew is in force in three towns in central Orissa, with some 800 police deployed and more to follow, the police said.
The fighting ignited on Monday when Christians put up a temporary arch to commemrate Christmas in Orissa's Kandhamal district where there has been continued tensions between the two sides.
Christians later attacked and injured a Hindu leader, known to resent Christian attempts to convert low-caste Hindus, police said.
During Tuesday and Wednesday, fighting and rioting continued sporadically, with Hindu temples and churches being set alight.
Government buildings and homes were also attacked.
The man who died was a Christian. No one has been arrested as yet.
A curfew on Wednesday night did not stop further small fights and stone throwing, although no injuries were reported.
Tensions had been high due to Christian missionaries finding the majority of their converts from "untouchable" Hindus - low caste Hindus who still face significant stigma.
Some hardline Hindus have accused Christian priests of bribing Dalits and poor tribespeople to convert.
Christian groups say that converts join Christianity willingly to remove themselves from the Hindu caste system.