Emergency services told the AFP news agency that the blast was caused by an improvised explosive device.
It occurred at the Malkohi camp for internally displaced persons (IDPs) on the outskirts of Yola in Adamawa state.
Yola has been seen as a relative safe place for those fleeing the violence.
The BBC's Chris Ewokor in Abuja says this is the first attack on a camp for IDPs in the north-east.
The explosion happened in a warehouse, emergency services say.
There are reportedly more than 1,000 children in the camp.
Two million people have been forced from their homes since the militants launched their insurgency in north-eastern Nigeria in 2009.
According to Amnesty International, at least 17,000 people have been killed in the conflict.
Although the militants have been forced out most of the territory they had seized, they are still active and there has been an upsurge in suicide attacks since President Muhammadu Buhari took office in May.
Teaching Boko Haram militants to play football
Who are Boko Haram?
At least three people have died when a bomb exploded at a camp in north-eastern Nigeria for people who have fled their homes because of the Boko Haram Islamist insurgency.