As many as 52 people are believed to have been injured, a military source told Reuters news agency.
The blast struck Jebo livestock market in Sabon Gari town in southern Borno at about 13:30 local time (12:30 GMT), sources said.
Suspected Boko Haram militants have have killed hundreds in the state.
It is not clear whether the explosion was caused by a suicide bomber or by a planted device.
Borno State has been at the centre of an Islamist insurgency, but in recent months Boko Haram has also targeted villages and towns in northern Cameroon as well as Chad and Niger.
Bombings intensified after the new Nigerian President Muhammadu Buhari vowed to crush the group. Since he was sworn in last May, more than 800 people have been killed.