Two other suicide bombers also reportedly blew themselves up at the gate of an internally displaced person (IDP) camp.
In its most lethal attack ever, Boko Haram claimed responsibility for the killing of at least 186 people in Kano on January 20, in coordinated bombings and shootings.
The report said that the woman blew herself up at market in the village Konduga, near the city of Maiduguri in North-Eastern Nigeria.
At least 80 people were injured and were rushed to the hospital in Maiduguri, a town about 30 kilometers (18 miles) away, he said.
In Nigeria, 28 people have been killed and 82 injured in three simultaneous suicide attackers in the town of Mandarari. "And in the confusion, the two other suicide bombers detonated in the market".
The Nigerian Army has launched a new mobile strike team aimed at reduction of ambushes and sudden deaths of their personnel even as they count down eighteen days to the capture of the king pin of the insurgency Abubakar Shakau.
But this year has seen a surge in attacks, including an audacious assault on an oil exploration team that killed 69 people in Borno in July, raising fears that Boko Haram is regaining strength.
Terror group Boko Haram is suspected to have carried out the attacks.
Authorities attributed the attacks on Tuesday to the Boko Haram militant group, Xinhua news agency reported.
The group has waged an eight-year war to create an Islamic state in north-east Nigeria, and provoked worldwide outrage by kidnapping more than 200 schoolgirls known as the Chibok girls in April 2014.
Ibrahim Liman, the head of a local anti-jihadist militia force, confirmed the details of the attack.