Oskar Gröning was found guilty in July 2015 of being an accessory to the murders of 300,000 people at the camp and sentenced to four years in prison.
"The prosecutor has rejected the application from the defence for a sentence suspension," court spokeswoman Kathrin Söfker told AFP, confirming local media reports.
A summons for the start of the sentence has not been issued, she said, adding that the prosecutor will make a decision separately on this.
Gröning's lawyer Hans Holtermann said he would appeal the decision as soon as possible, arguing that the doctor named by prosecutors had not done a proper examination.
Gröning has been living at home despite his conviction, and due to his old age, it has been unclear if he would actually be jailed.
But a court doctor has now determined that he is able to serve his sentence, on condition he is given appropriate nursing and medical care while in detention, said the spokeswoman.
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.
One million European Jews died between 1940 and 1945 at Auschwitz before it was liberated by Soviet forces.