They then went to the nearby camp for people displaced by Nigeria's conflict and simultaneously detonated their explosives.
The report said that the woman blew herself up at market in the village Konduga, near the city of Maiduguri in North-Eastern Nigeria.
A local medical source said that following the blasts a "huge number" of people were admitted to the Maiduguri hospital.
In Nigeria, 28 people have been killed and 82 injured in three simultaneous suicide attackers in the town of Mandarari. Two other bombers reported to have attacked a refugee camp located in the area.
As per reports the attack took place late Tuesday evening by fighting Boko Haram militants. But it has struck back with renewed zeal since June, killing at least 143 people before Tuesday's bombings and weakening the army's control.
Boko Haram has been fighting to set up an Islamic state since 2009.
Last month, an oil prospecting team was captured by al Barnawi's group. Boko Haram has killed more than 20,000 people in its eight-year insurgency. At least 37 people, including members of the team, died during the rescue operation.
Terror group Boko Haram is suspected to have carried out the attacks.
Boko Haram is a militant organization affiliated with the Daesh terrorist group, outlawed in many countries, including Russian Federation and the United States.
The attack prompted Vice President Yemi Osinbajo, who is standing in for President Muhammadu Buhari while he is on indefinite sick leave, to ask the military to step up its response.
It conducted large-scale attacks in northeastern Nigeria in 2009 and bombed a United Nations office in Abuja in 2011, killing 21 people.