Aid workers from Medicins Sans Frontieres and the Red Cross were among the victims.
The bombing took place at a camp in Rann, in Nigeria's northeast, near the border with Cameroon.
Reporting news of an incident the Nigerian military has described as "a mistake", TV news in Abuja described the unfolding disaster.
"News reaching us says a number of people are feared dead after a Nigeria Air Force plane reportedly dropped a bomb inside a settlement in northern Borno state. The incident, which the military has described as a mistake, is believed to have left scores of other people injured."
"Expressing regret for the action, defence spokesperson Brigadier General Rabe Abubakar told Channels TV that the incident did not occur in an IDP camp, as it has been reported in some quarters, but a settlement said to be occupied by civilians."
The Nigerian military says it ordered the bombing based on information that Boko Haram insurgents had gathered there.
Major General Lucky Irabor says he directed the strike, and described the mistake incident as the result of what he calls the "fog" of war.
"Unfortunately, the strike was conducted, but it turned out that locals somewhere around were affected. Among those that are wounded are local staff of Medecins Sans Frontieres as well as ICRC (International Committee of the Red Cross) so I thought that you should know very quickly for you to also disseminate."
Medicins Sans Frontieres has condemned the action.
"This large-scale attack on vulnerable people who have already fled extreme violence is shocking and unacceptable. The safety of civilians must be respected. We are urgently calling on all parties to ensure the facilitation of medical evacuations by air or road for survivors who are in need of emergency care."
The International Red Cross has confirmed a number of its staff were killed and wounded in a statement on Twitter.
"We report with sadness that among the casualties of today's airstrikes in Rann, 6 Red Cross staff were killed and 13 wounded. They were part of a team bringing desperately needed food for more than 25,000 displaced people in Rann. We are coordinating medical emergency efforts with relevant authorities and other aid actors."
