Bayvel, who was born on 28 March 1949 and had recently turned 71, played 10 Tests for the Springboks between 1974 and 1976, including all four against the touring All Blacks of 1976, a series the Boks won 3-1.
“It is with great sadness that we heard of Paul's passing,” said Mr Alexander.
“He was a formidable player and a person and will be remembered by all those who knew him.
“It is always sad to lose a family member and we want to wish the Bayvels, as well as his other family members and friends our sincere condolences in this time. Paul was a rugby man and part of our extended rugby family as well, so we are all poorer for his passing.”
Bayvel played all his provincial rugby for the Golden Lions, formerly Transvaal, as did two of his three brothers. Die-hard Lions fans will also fondly recall Bayvel's halfback partnership with legendary former Springbok flyhalf Gerald Bosch.