Reinhold Hanning was convicted for his part in the Holocaust, and died before a court could rule on his appeal
Reinhold Hanning, who was 95, was convicted last June but had appealed the judgement.
The presiding judge branded him a "willing and efficient henchman" in the Holocaust.
He was sentenced to serve five years for facilitating the killing of at least 170,000 people.
However, the conviction was not legally binding as appeals were still pending at Germany's highest court.
Hanning's sentence is likely to be one of the last handed out in Germany for World War Two-era atrocities.
According to German media reports, 28 prosecutions are under way against alleged war criminals and concentration camp guards, but the accused are generally over 90 years old.
Hanning, who was an SS guard at Auschwitz from 1942 to 1944, sat silently for much of his trial. But in April last year he apologised to several victims of the Nazis who were present in court, saying he was sorry and ashamed.
"I want to say that it disturbs me deeply that I was part of such a criminal organisation," he said.
"I am ashamed that I saw injustice and never did anything about it and I apologise for my actions. I am very, very sorry."
The Nazis killed about 1.1m people at Auschwitz in occupied southern Poland, most of them Jews.
Hanning was on duty at the camp at a time when hundreds of thousands of Hungarian Jews were murdered.
Around a dozen elderly Auschwitz survivors testified against him, giving harrowing accounts of their experiences.
Prosecutors said he had met Jewish prisoners as they arrived at the camp and may have escorted some to the gas chambers. Justice came late for Auschwitz survivors: Jenny Hill, BBC News Berlin Correspondent
By the time German law caught up with Reinhold Hanning he was a frail old man.
The pensioner who ran a dairy shop until his retirement was convicted last year of facilitating mass murder at Auschwitz.
There was no evidence to suggest he murdered prisoners himself, but the judge ruled that as an SS guard he was part of the Nazi machine and therefore helped to commit genocide.
Hanning's conviction was welcomed by Auschwitz survivors and prosecutors, who still hope to bring other former death camp guards to justice. But his death serves as a reminder that they're running out of time.
Holocaust survivor Joshua Kaufman (C) attended the Hanning trial, accompanied by his daughters Rachel (L) and Alexandra
Hanning's lawyer, Andreas Scharmer, said he had learned of his death on Tuesday evening. He declined to comment on the cause, merely noting that his client was very elderly.
Lawyer Thomas Walther, who acted for more than 20 joint plaintiffs in the case, said he was disappointed that Hanning had died before he could be imprisoned.
"If the judiciary had not been silent for decades, then there would not have been this disappointment," he said, adding that he had expected the conviction to be upheld in the next month or so.
Hanning is not the first death camp guard to die before he could serve prison time.
In 2011, Ivan Demjanjuk was convicted in a similar case, but also died before German's courts could rule on his appeal.