Most of the victims of the strike in Rann in the country's northeast on Tuesday were women and children, MSF said. Nigeria has said an air force board of inquiry will investigate the incident.
Military commanders have already called the bombing a mistake, blaming it on "the fog of war", saying the intended target was jihadists reportedly spotted in the Kala-Balge area, of which Rann is part.
The death toll could still rise further -- MSF said there were "consistent reports from residents and community leaders" saying that as many as 170 people were killed.
"This figure needs to be confirmed. The victims of this horrifying event deserve a transparent account of what happened and the circumstances in which this attack took place," MSF General Director Bruno Jochum said.
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Humanitarian workers were distributing food to between 20,000 and 40,000 people living in makeshift shelters at the camp when the bombing struck.
At least 20,000 have been killed and more than 2.6 million made homeless since the Islamists took up arms in 2009.
The air force said it had initially been given a list of 20 witnesses and said the inquiry board would report no later than February 2. No journalists have been allowed to visit the area of the bombing.
International aid agencies have condemned the bombing of civilians, who are facing extreme food shortages because of the conflict, as well as having lost their livelihoods and families.