The Pan Africanist Youth Congress (Payco) was disgusted that the Run Jozi night race was being held on Human Rights Day, it said on Wednesday.
"It is an insult to our heroes and heroines who perished on this day on March 21 1960 during the PAC [Pan Africanist Congress] led anti-pass campaign," Payco spokesperson Sello Tladi said in a statement.
"This race seeks to erase the PAC's impeccable liberation credentials from the memory of our people."
South Africans were celebrating Human Rights Day on Wednesday.
It was previously known as Sharpeville Day to commemorate the shooting of 69 black protesters by the police in 1960.
About 10 000 runners were expected to participate in the race, which would start on the Mandela Bridge at 7pm on Wednesday night.
Tladi said holding the race on Human Rights Day was disrespectful to those who had died during the Sharpeville protests.
Payco bemoaned the fact that the date for the Comrades Marathon had been changed because it fell on the Soweto Uprising commemoration on 16 June.
"[Those] who want to have fun and run like headless chickens in the streets of Johannesburg, should rather chose to do so on Valentine's day or Mandela day," said Tladi.