Cycling South Africa, the sport's national governing body, said Stander was riding Thursday in Shelly Beach when the vehicle struck him, CNN reported Friday.
"Not only is this a loss to South African sport, but we have lost a true gentleman who through his professionalism, modesty and humility, constantly showing sheer guts, represented our country with great pride," the cycling body said in a statement.
Stander, who recently married multiple South African road race champion Cherise Taylor, placed fifth in the Men's Cross Country mountain bike event at the London Olympics. He placed 15th in the same event four years earlier in Beijing.
Cycling South Africa said authorities were investigating the crash.