A rescue worker said the first blast happened at 11:10am local time (10:10 GMT) in Mashalari village of the Konduga area, about 40km from Borno state capital Maiduguri.
"[It] killed 15 people and left 43 others injured," he told AFP news agency. "It happened during aid distribution by an NGO, when people had gathered to receive donations."
"Twelve minutes later, another bomber struck, but luckily only she died," he said, speaking on condition of anonymity.
The rescue worker said both bombers were women but did not specify which NGO was distributing aid.
Babakura Kolo, from the Civilian Joint Task Force, a militia assisting the military with security, confirmed the rescue worker's account.
"We have dispatched out a team to the scene," he said.
Bello Dambatta, head of rescue operations for Borno state's Emergency Management Agency, said women were the majority of those killed in the morning attack and the death toll was likely to rise.
No immediate claim of responsibility came for the attack, but the Boko Haram armed group has carried out similar bombings in the past in the region.
Northeastern Nigeria is in the grip of a humanitarian crisis caused by Boko Haram violence, which has left at least 20,000 people dead and displaced more than 2.6 million since 2009.
The violence has devastated farming, leading to chronic food shortages and leaving hundreds of thousands of people on the brink of starvation and dependent on aid agencies for help.
Nigeria's military and government maintain that Boko Haram is a spent force as a result of a sustained counterinsurgency campaign over the last two years.
But continued attacks, particularly in hard-to-reach rural areas of Borno, suggest claims of outright victory are premature.
On Saturday, at least 28 people were killed and more than 80 wounded when three female suicide bombers detonated their explosives outside a camp for displaced people in Konduga.
This month, Boko Haram fighters fired a rocket-propelled grenade into a camp for internally displaced persons near the border with Cameroon, killing seven.
Amnesty International says Boko Haram attacks since April have killed nearly 400 people in Nigeria and Cameroon - double the figure of the previous five months.
The UN children's fund said last month 83 children had been used as suicide bombers this year, four times as many as in all of 2016.