Police spokesman for Borno state, where the attacks took place on Saturday, said the bombings in the town of Biu also injured over 50 people.
It was not clear how many people were killed in the first attack, which came when a woman waiting in an aid distribution line detonated her explosives, and how many in the second one, which came nearby and caused little or almost no fatalities.
Those killed in the first attack were people affected by the eight years of Boko Haram insurgency, which has killed 20,000 people and left millions displaced in northeastern Nigeria and the neighboring countries.
Mohammed Maliya, a member of the aid team in Biu, said the woman who carried out the attack appeared relaxed and was eating a banana while waiting in line with others. She and the other woman were killed in the attacks.
Boko Haram normally uses women and girls to carry out attacks in northern Nigeria, especially now that the group has been pushed out of its old bastions in and around the provincial capital of Maiduguri. Biu, where the Saturday attacks happened, is about 185 kilometers (115 miles) from Maiduguri.
The Nigerian government claims that its massive counterinsurgency offensive in 2015 has rendered Boko Haram a spent force but it has faced criticism as the militant group still carries out assaults on civilians in crowded places in Borno and other places.
The skepticism about Nigeria’s success in rooting out Boko Haram has been exacerbated by a recent government declaration that it plans to gather civilians inside fortified garrison towns in the future and leave the militant group operating in the countryside.