The 66-year-old had appeared to be in remission after visiting India earlier this year to receive robotic radiation treatment in Bangalore.
Rice's family confirmed his death to South Africa's Eye Witness News, saying he was admitted to hospital on Sunday with severe stomach pains.
The all-rounder captained South Africa at the age of 42 on their historic post-isolation limited overs tour of India in 1991, but was then controversially left out of the squad for the World Cup in Australia and New Zealand the following year.
He also briefly represented Scotland before the Proteas' readmission to international cricket.
Rice was prolific with both bat and ball and considered one of South Africa's greatest ever all-rounders.
He played in 482 first-class matches for Transvaal, Natal and Nottinghamshire, scoring 26,331 runs at an average of 40.95. He also took 930 wickets at 22.49 apiece before retiring in 1994.
Rice led Nottinghamshire to the County Championship titles in 1981 and 1987, and was named Wisden Cricketer of the Year after the first championship success.
He is credited too with helping persuade Kevin Pietersen to qualify to play international cricket for England.
(Reporting by Nick Said; editing by Amlan Chakraborty)
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