MSF said the strike occurred in Rann in Borno state, the epicenter of the jihadist group's seven-year-old bid to create an Islamic caliphate. Regional military commander General Lucky Irabor located it at Kala Balge, a district including Rann.
Irabor, who said it was too early to determine the cause of the mistake, told journalists an unknown number of civilians had been killed, adding that humanitarian workers from MSF and the International Committee of the Red Cross (ICRC) were injured.
"MSF teams have seen 120 wounded and 50 dead following the bombing," said Charlotte Morris, a spokeswoman for the medical charity. "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."
A spokeswoman for ICRC said six Nigerian Red Cross members were killed and 13 were wounded.
The insurgency has killed more than 15,000 people and forced two million to flee their homes, many of whom have moved to camps because it has been too dangerous to return home.
The air strike came amid an offensive against Boko Haram by Nigeria's military over the last few weeks. President Muhammadu Buhari said last month a key camp in the jihadist group's Sambisa forest base in Borno state had fallen.
A statement issued by the presidency said the air strike was a "regrettable operational mistake" that happened during the "final phase of mopping up insurgents in the northeast".
Boko Haram has stepped up attacks in the last few weeks as the end of the rainy season has enabled its fighters to move more easily in the bush.
A video featuring an audio recording purporting to be Boko Haram leader Abubakar Shekau, which was posted on social media late on Monday, said the group was behind twin suicide bombings at a university earlier that day which killed two people and injured 17 others.
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