In one of the last cases against a surviving Nazi, Oskar Gröning was found guilty in July 2015 of being an accessory to the murders of 300,000 people at the death camp.
Gröning has been living at home despite the conviction as his defence team mounted an appeal against his four-year jail sentence, arguing that imprisonment at such a high age would violate his "right to life".
But Germany's Constitutional Court on Friday said Gröning's "complaint against the refusal to postpone the execution of the prison sentence was unsuccessful".
It found that appropriate health care could be provided in prison and that "if there are any adverse changes in health during imprisonment, the jail term can be interrupted".
"The high age of the applicant is in itself not sufficient to refrain from enforcing the criminal penalty," said the court.
The court also stressed that Gröning has been found guilty of "complicity in murder in 300,000 cases, something that lends particular weight to the enforcement of the punishment".
More than one million European Jews were killed at Auschwitz before it was liberated by Soviet forces.
Yet of the camp's 6,500 SS personnel who survived the war, fewer than 50 were ever convicted.
Gröning worked as an accountant at Auschwitz, sorting and counting the money taken from those killed or used as slave labour, and shipping it back to his Nazi superiors in Berlin.
He was also on several occasions assigned to "ramp duty", processing deportees as they arrived by rail in cattle cars.
During his trial, Gröning acknowledged "moral guilt" but said it was up to the court to rule on his legal culpability.
He had previously been cleared by German authorities after lengthy criminal probes dating back to the 1970s.
But a case was reopened against him after the legal basis for prosecuting former Nazis changed in 2011 with Germany's landmark conviction of John Demjanjuk.
Demjanjuk, a former death camp guard, was sentenced not for atrocities he was known to have personally committed, but on the basis that he worked at the Sobibor camp in occupied Poland and had thus been a cog in the Nazis' killing machine.
Demjanjuk died in 2012 before his appeal could be heard, but that verdict spurred new investigations against several elderly former Nazis.
Among a handful of convictions since has been that of Reinhold Hanning, found guilty of complicity in the mass murders at Auschwitz.
He died aged 95 this year, before he could serve his jail term.
A case against former SS medic Hubert Zafke collapsed in September after the court found that the 96-year-old was unfit to stand trial.
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