The explosion happened about 1.30pm in the town of Sabon Gari, in Borno state, which is the heartland of the Islamist militant group.
“So far 52 people are injured, 47 dead persons have been removed from the market,” Umar Kidda, a member of a civilian vigilante group, told Reuters by telephone.
Kidda, who saw bodies being taken away, said the market had been busy when the explosion occurred.
A military source who declined to be named said about 50 people had died.
The US state department strongly condemned what it said was a terrorist attack in Borno.
“While no individual or group has yet claimed responsibility for the attack, it took place in an area where hundreds of people have been killed in recent weeks by suspected members of the terrorist group Boko Haram,” it said.
Boko Haram has killed thousands of people during a six-year armed campaign to set up an Islamic state in north-eastern Nigeria.
Reuters says more than 600 people have been killed in raids and bombings by the insurgents since the president, Muhammadu Buhari, took office on 29 May, promising to crush the group.
At the start of the year Boko Haram controlled territory about the size of Belgium.
The army said it had pushed the group from most of that area in the past few months with the help of troops from Chad, Niger and Cameroon, but there had been a recent resurgence in militant attacks.
No one claimed immediate responsibility for Tuesday’s explosion.