Isa Yuguda, the Bauchi state governor, said: "The security agencies have been directed to deal decisively with the perpetrators of this mayhem."
Hundreds of people died in Jos, the capital of neighbouring Plateau state, last year, in violence between Muslim and Christian gangs sparked by a disputed election.
Jos lies at the crossroads of Nigeria's Muslim north and Christian south.
The fighting was considered the worst unrest in Africa's most populous nation for several years.
Security forces in Plateau state were on high alert as a result of the deaths in Bauchi.
"We have placed security here in Jos on red alert. We want to forestall any eventuality here," Dan Manjan, a spokesman for the governor of Plateau state, said by telephone.
Nigeria is roughly equally split between Christians and Muslims, although traditional animist beliefs underpin many people's faith.
More than 200 distinct ethnic groups generally live peacefully side by side in the West African country, although civil war left one million people dead between 1967 and 1970 and there have been bouts of religious unrest since then.