Mr Getty, 47, was found dead in the bathroom of his Hollywood Hills residence on Tuesday afternoon.
The Los Angeles coroner's office said initial reports suggested natural causes or an accident was to blame.
A statement from Ann and Gordon Getty confirmed that Andrew, one of their four sons, had died.
His oil baron grandfather died in 1976. Industrialist J Paul Getty founded the Getty Oil Company and was once named the richest living American by Fortune magazine.
Jack Richter of the Los Angeles Police Department (LAPD) told reporters that officers went to the home shortly after 14:15 local time (22:15 GMT) on Tuesday.
They found the body in the bathroom and interviewed a woman who was present.
The woman, who has not been identified and is not under arrest, had called officers to report that someone had died at the gated home on Montcalm Avenue.
Los Angeles County coroner's assistant chief Ed Winter told local media that medication had been found at the scene.
"The tentative information that we do have is that he was not feeling good for the last couple of months and he supposedly had an appointment tomorrow with a personal physician," Mr Winter said.
"He had some medication that we recovered and don't know if he had taken the medication or what his medical history is. We do have a doctor's name that we're also going to follow up."
He said toxicology tests could take a number of weeks.
The LA Times quoted one law enforcement source as saying Mr Getty had suffered a blunt-force trauma but it was unclear how the injury had been caused.
LAPD spokesman Commander Andrew Smith said: "At first glance, it does not appear to be a criminal type of act. But that could change."
Andrew Getty, the grandson of J Paul Getty and one of the heirs to the family fortune, has been found dead at home, his parents have confirmed.