Four witnesses told Reuters near the scene that a woman had entered the roadside trading area behind the city's main market before blowing herself up.
"While the people were trying to help the injured, the second bomb blasted," witness Sani Adamu told Reuters, "I saw lots of bodies."
An official at the National Emergency Management Agency (NEMA) said 21 bodies had so far been removed from the scene of the twin blasts, while a medical worker said a local hospital where he was based had received some 13 bodies.
Nigerian authorities did not immediately respond to requests for comment. There was no claim of responsibility, but suspicion is likely to fall on violent Islamist group Boko Haram, whose five-year campaign for an Islamic state has killed thousands.
The group has increasingly used female suicide bombers.
In June, there were four attacks by female bombers in the largely Muslim north, including one targeting a school in Kano, the region's biggest city.
Another woman blew herself up at a teacher training college in Nigeria's central Niger state on Nov. 12, killing at least one other person.
Adamu said he counted more than 30 people on the ground, but did not know if they were dead or wounded. Police cordoned off the scene and sirens wailed in the aftermath.
Boko Haram has stepped up assaults in the northeast of Nigeria since it rejected government claims of a ceasefire last month, showing it remains the biggest security threat to Africa's biggest economy and top oil producer.
Borno state, of which Maiduguri is the capital, has seen some of the fiercest fighting, although the city itself had not witnessed a suicide bombing since July.
Nigerian President Goodluck Jonathan plans to ask the national assembly to extend a state of emergency in the three northeastern states worst hit by the insurgency when it expires this month.
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