Oskar Groening, 96, known as the “bookkeeper of Auschwitz”, argued his imprisonment would violate his right to life.
But a German court ruled on November 29 that Mr Groening was fit to go to prison and rejected his plea for the sentence to be suspended.
Mr Groening, who is physically frail, was sentenced to four years in prison in 2015, in one of the last cases against a surviving Nazi.
But he has not been incarcerated since then because of the legal argument about his health.
His lawyer, Hans Holtermann, said that the latest legal challenge asked Germany’s constitutional court to determine if imprisonment would violate Mr Groening’s right to life, given his medical condition.
He told the broadcaster that an expert had concluded that Mr Groening was not fit enough to be imprisoned.
The November 29 court ruling had said that enforcing Mr Groening’s sentence would not breach his fundamental rights and added that special needs related to his age could be addressed in prison.
Mr Groening, a former Nazi SS officer, did not kill anyone while working at the camp in Nazi-occupied Poland.
But a court convicted him in 2015 of aiding and abetting mass murder there through various actions, including by sorting banknotes seized from arriving Jews.
He admitted during his trial that he was morally guilty and said he had been an enthusiastic Nazi when he was sent to work at Auschwitz in 1942 at the age of 21.
At least six million Jews were murdered during the Holocaust carried out under Adolf Hitler.