Oskar Groening was found guilty in July 2015 of being an accessory to the murders of 300,000 people at the Nazi death camp.
But he filed an appeal for the sentence to be suspended.
"Based on expert opinion, the superior regional court finds that the convicted individual is fit to serve out the term despite his advanced age", said the court in Celle in northern Germany.
Incarcerating Groening would not violate his fundamental rights, it said, arguing that "appropriate precautionary measures" could be taken to meet any special needs arising from his old age.
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Making the case for his imprisonment, German prosecutors have said that a court doctor has determined that Groening is able to serve his sentence, on condition he is given appropriate nursing and medical care while in detention.
Groening 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.
More than one million European Jews died between 1940 and 1945 at Auschwitz before it was liberated by Soviet forces.
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