The bombing happened in the north eastern Rann, near the border with Cameroon. It is believed to be the first time Nigeria`s military has admitted to making such a mistake.
Military commander Major General Lucky Irabor said he ordered the mission based on information that Boko Haram insurgents were gathering, along with geographic coordinates.
It is too early to say if a tactical error was made, he said.
In a statement Doctors Without Borders (MSF) said: "MSF confirms that a bombing by the Nigerian Army has occurred in an internally displaced person camps in Rann, Nigeria.
"MSF teams have seen 120 wounded and 50 dead following the bombing. "Teams are trying to provide emergency first aid in its facility and are stabilizing patients to evacuate wounded.
"Our medical and surgical teams in Cameroon and Chad are ready to treat wounded patients. "We are in close contact with our teams, who are in shock following the event."
The International Committee of the Red Cross said the workers who were killed were "part of a team bringing desperately needed food for more than 25,000 displaced people in Rann".
The charity added it is "coordinating medical emergency efforts with relevant authorities and other aid actors" in Nigeria.
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