Court officials in Munich said the retired Cleveland-area autoworker had a fever that would not fall even after medication was administered, the BBC reported.
The trial resumes Dec. 21, the court said.
Prosecutors charge Demjanjuk worked as a guard at the Sobibor extermination camp in Nazi-occupied Poland in 1943 and helped force 27,900 Jews to their deaths in the Holocaust. Demjanjuk maintains he was a Soviet soldier captured by the Germans and spent most of the war in prison camps.
Demjanjuk's lawyer has argued that his client should not be tried because of his poor health. Holocaust survivors have said Demjanjuk, who lost his U.S. citizenship when he was deported in May, is playing up his illness, the British broadcaster said.
Wednesday's proceeding was to have included testimony from 40 relatives of victims of Sobibor. A lawyer for some members of the group said they were "slightly frustrated" by the postponement, the BBC said.
The trial is expected to last until May. If found guilty, Demjanjuk could be sentenced to 15 years in prison.