The human rights organisation has provided the ABC with a statement that contains credible and specific details about an incident involving the beating and mistreatment of five inmates in September.
As a result of one prisoner's injuries, he underwent an emergency amputation.
Andrew Beswick of from Amnesty is calling on the military government to abide by international norms of justice and stop tolerating the culture of impunity.
"Our concern is that we've received reports about five men who had escaped from prison and were recaptured and subsequent to that they were taken to barracks and repeatedly beaten by military officers," he said.
"We're talking about them being repeatedly beaten, one man was damaged so badly that his leg had an open fracture on it, and that leg later had to be amputated.
"Another man was attacked with a gun and was in fact anally raped and that caused severe internal injuries."
The ABC's PM program has two documents that Amnesty says verify the torture allegation.
One describes a litany of ailments suffered by the victim with the most serious injuries.
He's a 30-year-old man who was beaten and left without medical treatment until it was too late to save his right leg.
It had been badly fractured - and when he was finally admitted to hospital, doctors identified necrosis, or infected and dead skin.
They had to amputate to save his life.
His lower jaw was fractured and needed to be wired shut.
Amnesty's Andrew Beswick says the assault against all five men lasted over two days.
"It's fairly shocking when you go into the detail of it," he said.
"We know that they were taken into a room, they were forced to take their clothes off and left naked in the dark."
"They were hit with the butt of guns, they were sworn at, they were spat on. They had hot water poured on them and, as I said, one of the men was assaulted with a gun."
Amnesty is calling on the Australian and other international governments to pressure Fiji to address the culture of impunity in the military, and the broader culture of fear operating in other parts of Fiji's justice system.
"I think there's definitely a climate of intimidation generally," he said.
"Press is extremely restricted in Fiji. There's concerns about interference in matters before the court.
"I think, you know, people are generally reluctant to speak out on these issues and so it's important that when we do have that information that it is brought to the attention of the government."
The ABC contacted the office of the Attorney-General of Fiji in Suva with a series of questions, but has yet to receive a reply.
Fiji issued a statement responding to the allegations made by Amnesty. Significantly, the regime neither explicitly denies the assault, nor that the perpetrators were soldiers.
It read, in part: "The matters raised are before the courts. The judicial process is independent and it is not appropriate for the government or any other party to comment or conduct a 'trial' outside this process.
"If these prisoners have complaints about the way in which they were treated in custody, it is for their legal representatives to raise these complaints.
"The Fijian government does not condone the use of excessive or disproportionate force in the apprehension of escaped prisoners.”