They say a church in Peri village near Potiskum, the economic capital of Yobe, was set on fire in an attack late on Christmas Eve.
No group has so far said it carried out the attack.
The Boko Haram Islamist militant group has targeted a number of churches in the north since 2010.
It has killed hundreds in its campaign to impose Sharia law.
A series of bomb attacks carried out by the group across the country at Christmas 2011 – including two at Christmas Day church services – left almost 40 people dead and many more injured.
‘Savage acts of terrorism’
The head of the Network for Justice human rights group, Zakari Adamu, told the BBC that the gunmen also attacked the homes of Christians following the attack during the midnight mass service.
The AFP news agency reported that the pastor of the church – a branch of the Evangelical Church of West Africa (ECWA) – is among the dead.
Military Spokesman Eli Lazarus told the Reuters news agency that six people were killed in the violence, which happened when “unknown gunmen attempted to attack Potiskum but were repelled by troops”.
“While they were fleeing, they attacked a church in a village,” he said.
The military say that a suspected gunman has been detained, and security in the area has been stepped up to reassure residents.
They could not say how many gunmen took part in the attack or whether they belonged to a particular organisation.
The violence comes on the same day that the Pope – as part of his Christmas Day address – prayed for harmony in Nigeria, lamenting what he called “savage acts of terrorism” that frequently target Christians.
The head of the Christian Association of Nigeria in Yobe, Idi Garba, told AFP that many worshippers at ECWA “are still missing”.
“I have been informed that six bodies have been recovered,” Mr Garba said.
He said that some worshippers who lived near the church “fled their homes during the attack and it is assumed that they are still hiding in the bush”.
Correspondents says that while Yobe’s population is overwhelmingly Muslim, Potiskum has a significant Christian minority. Peri is just 2km (1.24 miles) outside the city.
Boko Haram has been able to carry out so many attacks in Yobe because it borders Borno state where the insurgent group is based.
Nigeria is Africa’s most populous state and its biggest oil producer. Most people in the south are Christian, whereas the north has a Muslim majority.