The Lüneburg judge said that Gröning was too sick to get out of bed and had not been able to make it to the process in the morning, stressing that there was no evidence that the defendant was faking his condition.
Gröning will now be examined by his home physician as well as one appointed by the court to determine his condition and how the trial should proceed, said court spokeswoman Frauke Albers. The trial could resume as usual next Tuesday if it is possible.
Given the advanced age of most German war crimes suspects, Gröning is expected to be among the last to face justice, 70 years after the liberation of the concentration camps at the end of the Second World War.
Prosecutors said Gröning served as an accountant, who sorted and counted the money taken from those killed, collecting cash in different currencies from across Europe.
He also performed "ramp duty", guarding the luggage stolen from deportees as they arrived by rail at the extermination and forced labour camp in Nazi-occupied Poland, they said.
Determining if defendant is "unfit for trial"
The ageing defendant had to cancel a trial hearing for the first time on Wednesday due to poor health.
If the court doctor determines Gröning to be unfit to stand trial, there are three possibilities. First, the court may suspend the trial for up to three weeks without any major consequences.
However, if the break lasts longer than the three weeks, the second possibility is that the process would have to start over, with witnesses having to testify again.
The third possibility depends on whether the defendant's condition is determined to be altogether too poor in the long-term.
"The court could also in principle find the defendant to be permanently unfit. Then the case against him would be definitively closed," Albers said.
Gröning's attorney said that the question of his client's health was "for the doctor" to determine.
The plaintiffs' attorney Thomas Walther was very critical of what he said was the German justice system's longstanding inaction of justice.
In 1985, a Frankfurt court had decided not to prosecute Gröning, as well other concentration camp workers, because it said the work of SS guards on the ramp did not play a major part in the murder of Jewish people.
"If the German justice system - and in particular the Frankfurt justice system - had not failed in the way they have until now, we would not be in this process against Gröning in the year 2015 like we are now," Walther said.
Walther is representing more than 50 of some 60 plaintiffs, many of whom are Auschwitz survivors.
Asking for forgiveness
At the beginning of the trial, Gröning admitted having "moral guilt" in the atrocities and asked for forgiveness.
Gröning is being tried on 300,000 counts of "accessory to murder" in the cases of deported Hungarian Jews who were sent to the gas chambers, and faces up to 15 years in jail.
The former SS guard has been open about his work and experiences during the Second World War, first speaking up in 1985 when a member of his stamp collectors' club handed him a book written by a Holocaust denier.
He returned the book with a message saying "I saw everything. The gas chambers, the cremations, the selection process... I was there."
He later wrote a memoir for his family, recounted his memories in the German media and appeared in a BBC documentary.
German courts had previously cleared Gröning, but the legal basis changed in 2011 with the trial of former death camp guard John Demjanjuk, who was convicted solely on the basis of having served at a camp.
Before that, courts had only punished defendants for individual atrocities.
Some 1.1 million people, most of them European Jews, perished between 1940 and 1945 in the Auschwitz-Birkenau camp before it was liberated by Soviet forces.