Muir, originally from Kimberley, became the youngest person in the world to swim what was then the 110m backstroke (now 100m) in 1:08:70 on August 10, 1965, Beeld reported.
She broke the record, aged 12, at the amateur swimming federation's national junior competition in Blackpool, England.
In the next five years, she established 15 new world records in the 110m and 220m backstroke.
In 1980, she was inducted into the International Swimming Hall of Fame.
Muir gave up swimming when she was in matric to focus on her studies. She later became a medical doctor and ran successful medical practices in South Africa and in Canada.
According to Beeld, Muir had been battling breast cancer since 2009, and had been told by her doctors that the cancer had spread to other parts of her body.