The aircraft was on a mission against Boko Haram extremists when the accident happened in north-east Rann, near the border with Cameroon.
Many Christians who have been displaced by extremists Muslims have been living in the camp.
Military commander Major General Lucky Irabor confirmed the accidental bombardment and accepted that Nigerians working for Doctors Without Borders and the International Committee of the Red Cross are among the wounded.
This is believed to be the first time Nigeria's military has admitted to making such a mistake.
