Rice, who had been suffering with a brain tumour, passed away in a Cape Town hospital on Tuesday.
Nottinghamshire, the county that Rice served for many years, announced in a statement: “Nottinghamshire County Cricket Club is saddened to announce that former captain and cricket manager Clive Rice has passed away aged 66.”
Rice played for Nottinghamshire in the 1970s and 1980s and in his debut season took 53 wickets and scored 1,128 Championship runs.
He linked up with Sir Richard Hadlee at the county following the New Zealander’s arrival at Trent Bridge in 1978 and forged a 10-year partnership which secured many honours for the club.
Rice played for South Africa in a number of unofficial Tests during the 1980s while South Africa were excluded from international cricket owing to the sporting boycott of the country due to its apartheid laws.
He also captained the Proteas in their first one-day international and continued playing first class cricket until his retirement in 1994, finishing his career at Natal.
Rice later encouraged Kevin Pietersen, as a talented teenager with a South African passport, to join Nottinghamshire in 2000. Pietersen, who went on to international honours with England, wrote in his autobiography that Rice was “a great early influence on me”.
Nottinghamshire added in their statement on Tuesday: “Our thoughts are with his family and friends.”