Aid workers who had been working with the 25,000 displaced people in Rann were among the dead.
"Six staff members or volunteers with the Nigerian Red Cross were killed and 13 were wounded," said Jason Straziuso, a spokesman for the International Committee of the Red Cross.
According to Irabor, the bombardment happened during an operation to target Boko Haram militants in the area.
"Unfortunately, the strike was conducted but it turned out that other civilians were somewhere around the area and they were affected," he told reporters in Maiduguri.
Nigerian president Mohammadu Buhari called the strike "a regrettable operational mistake" in a statement.
Much of the Nigerian military's campaign against Boko Haram has been conducted using attack helicopters and fighter jets that fly over vast stretches of the northeast.
That has long posed a human rights dilemma, as militants are frequently difficult to isolate from the civilians held against their will in insurgent encampments. Some victims of Boko Haram have reported that the Nigerian military shot indiscriminately at those encampments during offensive operations, killing both militants and kidnapped civilians in the same stream of gunfire.
This is the first time during Nigeria's three-year campaign against Boko Haram that the military has acknowledged a large number of civilians killed in a mistaken bombardment. It remains unclear how the military could have misidentified a camp where 25,000 displaced people were living with a terrorist enclave.
In recent months, the Nigerian military has fought with Boko Haram fighters in Rann, who had attacked troops with improvised explosive devices, suicide bombers and ambushes.