A military spokesman told the BBC two vehicles were driven into the barracks in Jaji in what he described as "surprising and an embarrassment".
It is not clear who was responsible for the attack.
But the army suspects Islamist militant group Boko Haram, which has recently targeted churches in the state.
The group is fighting to overthrow the government and impose an extreme form of Sharia, or Islamic law.
The BBC's Will Ross in Lagos says that while Christians and churches are frequently targeted, this incident looks more like a direct attack on the military.
On Friday, Nigeria's military offered a reward of 50m naira ($317,000; £197,709) for help in tracking down suspected Boko Haram leader Abubakar Shekau, and 10m each for other suspected leaders of the group.
'Curious worshippers' The military said a bus entered the barracks and was driven into the wall of the church where it exploded.
Ten minutes later, a car blew up outside the church.
"The first blast caused no casualties and curious worshippers gathered around the scene looking at the debris... and that was when the second blast happened," the military spokesman said.
Eyewitnesses reported seeing bodies at the scene, and people being carried away on stretchers.
At least 50 people were killed in bombings in Kaduna in June and the reprisals that followed.
And almost a month ago seven people died in a suicide bombing at a Roman Catholic church in the state.
Kaduna is on the dividing line between Nigeria's mainly Christian south and the north, which has a large Muslim majority.