More than 100 people, many of them children, were injured in the bombing at a camp for people displaced by the Boko Haram insurgency in Rann, in the country's northeast, on Tuesday.
Six local Red Cross workers who were distributing food to between 20,000 and 40,000 people living in makeshift shelters at the camp were among the dead.
The Nigerian Air Force said a board of inquiry comprising six senior officers would investigate the bombing, and had initially been presented with a list of 20 witnesses.
The board will submit its report no later than February 2, it added.
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Military commanders have already called the bombing a mistake, blaming it on "the fog of war".
They said the intended target was jihadists reportedly spotted in the Kala-Balge area, of which Rann is part.
The Nation newspaper, sympathetic to President Muhammadu Buhari, attributed the bombing to a "failure of intelligence" caused by information provided by a "foreign country", without elaborating.
At least 20,000 have been killed and more than 2.6 million made homeless.
On December 24, Nigeria said it had flushed Boko Haram fighters from their stronghold in the Sambisa Forest of Borno state and that the group was in disarray. But attacks on troops and civilians continue.
Alfred Davies, a field coordinator for Doctors Without Borders (MSF), and one of the injured victims who spoke to AFP, said the air force dropped at least two bombs.
"The plane circled back and it dropped a second bomb five minutes later," he said, adding that they were "dropped on houses".
He added: "There are no words to describe the chaos. Some people had broken bones and torn flesh; their intestines hanging down to the floor. I saw the bodies of children that had been cut in two.