Further, vast wealth is believed to have been left in trust before he died, the newspaper reported.
The former chairman of the Anglo American Corporation and De Beers died in August, aged 92.
"Almost everything in the will has been left to his widow Bridget, to whom he was married for 57 years," the report said.
This includes his extensive art collection, his stud farm in Kimberley and all his racehorse enterprises, several property and company investments, stocks and cash.
"But nowhere in the will is there any mention of other Oppenheimer billions."
The Star report said no mention was made in the will of his son Nicholas, chairman of De Beers; his daughter Mary; or his five grandchildren and two great-grandchildren.
"But it is known that they have not been left high and dry and have probably benefited from those trusts."
The Star further reported that R1 million had been left to the Bridget Oppenheimer Trust.
"Mrs Oppenheimer has a number of endeavours and fields, mainly relating to women, to which she directed funds."
Also included in Oppenheimer's will were his eight godchildren - mostly children of former or present Anglo American staff - each set to benefit by R50 000.
Oppenheimer took over the family's interests and De Beers in 1957, building them up to become among the world's foremost mining and industrial corporations.
He retired as chairperson and director of Anglo American in 1982 and as chairperson of De Beers in 1984, after 27 years in that post. He retired as a director of De Beers in 1994, after 60 years on the board.
The executors named by Oppenheimer are three of his former business associates as well as friends, Isle of Man-based David Edward Salmon, and Michael Julian Hendry and Clifford Thomas Elphick, both of Johannesburg.
The Brenthurst Library in Parktown is known for its unique collection of art and Africana, which have now been bequeathed to his widow. - Sapa