The girl approached a crowd buying noodles from a food vendor in the Customs area of the city around 9:30 pm yesterday and detonated her explosives, they said.
Although no one has claimed responsibility the attack bore the hallmark of Boko Haram Islamists who are notorious for using suicide bombers, mostly women and young girls, in attacking civilian targets.
"The girl walked towards the crowd but she blew up before she could reach her target," said witness Grema Usman who lives in the area.
"(Judging) from her corpse the girl was around 10 years old," Usman said.
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An aid worker involved in the evacuation of the body gave a similar estimate of the bomber's age.
"The girl was clearly not more than 10 and this could have made her too nervous, making her to detonate the explosives prematurely," the aid worker suggested.
Borno state police spokesman Victor Isuku, meanwhile, said a second female suicide bomber was caught and lynched by an angry mob. Her bomb was safely detonated by security forces, he said.
Authorities blamed the attack on Boko Haram, whose seven-year insurgency has killed 20,000 people and displaced 2.6 million others. The conflict has spilled into Nigeria's northern neighbours.
Yesterday's attack came a week after Nigerian President Muhammadu Buhari said the jihadist group had been routed from Sambisa forest, its last stronghold in Borno state.