Officers near Kaiserslautern, Rhineland Palatinate, originally stopped the car at around 1am because it seemed to be driving around aimlessly.
The driver was the dead man's 26-year-old son, while his 47-year-old wife and 21-year-old daughter were also passengers.
Senior public prosecutor Helmut Bleh said that the man had been mentally ill and was severely emaciated, the Der Spiegel magazine reported on Friday.
The family said he had refused to eat. An autopsy has been scheduled to confirm the cause of death.
The man had died on Tuesday morning, but the family did not inform anyone of the death. Instead they drove around "completely confused" with the corpse. The son told police he had considered dropping off his dead father's body in front of a hospital, said Bleh.
He said the three family members were being investigated for failing to render assistance. People are legally obliged to help a family member in need, he said, and the family were aware of the father's rapidly deteriorating condition but failed to seek medical attention.
In 2009, a lawyer had been appointed to oversee the man's health care, yet even he apparently failed to notice the dramatic and ultimately fatal developments. Prosecutors said they would be investigating whether the attorney had fulfilled his obligations.