"Others were reportedly shot in the leg during interrogation, provided no medical care and left to bleed to death," the London-based human rights group said in a new report.
More than 950 people died in military custody in the first six months of this year, according to "credible information" from a senior Nigerian army officer, it said.
Senior Ministry of Defence officials at a meeting with Amnesty officials in July denied knowledge of one case in which soldiers on April 19 deposited 60 bodies at the mortuary of the Sani Abacha Teaching Hospital in Damaturu, the capital of Yobe state, claiming they were Islamic extremists killed in a shootout.
But a source close to the military interviewed by Amnesty International said the 60 had been "taken out of their cells and shot and killed by soldiers." They had been detained at the Presidential Lodge guardroom in Damaturu.
The senior officers said they would investigate if they received written details of the allegations. Amnesty International said it sent details in September but has not received a response.
A military spokesman did not immediately respond to phone calls seeking comment on Tuesday, a public holiday as Muslims celebrate the feast of Eid al-Adha.
The killings and deaths documented by Amnesty International may help answer questions raised by an Associated Press report in August that detailed how hundreds of detainees have gone missing since the military imposed a state of emergency on May 14 on the three northeastern states that cover one-sixth of Nigeria.
The AP report said hundreds of people were being rounded up, often indiscriminately, in night raids. It said distraught relatives, human rights organizations and journalists have asked the army, the police, intelligence services and government officials where the arrested people are, but answers have not been provided. The number of people detained is also unclear.
In an atmosphere of deep suspicion and fear, those detained can easily be identified as being suspected Boko Haram members.
Amnesty International said those killed all were detained as suspected members or associates of the Boko Haram terrorist network that has claimed responsibility for attacks that have killed hundreds of Muslim and Christian civilians this year in their mission to overturn democracy and force Nigeria to become an Islamic state. This West African nation, Africa's biggest oil producer and most populous of some 160 million people, is almost equally divided between the predominantly Muslim north and mainly Christian south.
Most deaths recorded by Amnesty International took place at the Presidential Lodge guardroom and a detention centre called Sector Alpha and nicknamed "Guantanamo" in Damaturu, and at Giwa Military Barracks in Maiduguri, the capital of Borno state and the birthplace of Boko Haram.
An AP reporter who was in Maiduguri saw military ambulances arriving at the mortuary of the main hospital in Maiduguri on an almost daily basis.
"Hundreds have been killed in detention either by shooting them or by suffocation. People are crammed into one cell. There are times when people are brought out on a daily basis and killed," Amnesty International quoted a second senior officer in the Nigerian army as saying.
The organization called for an urgent investigation.
"This is a staggeringly high figure that requires urgent action by the Nigerian government," said Lucy Freeman, Amnesty's deputy Africa director. "The details of what happens behind locked doors in these shadowy detention facilities must be exposed, and those responsible for any human rights violations brought to book."
Nigeria's military is notorious for extrajudicial killings of civilians.