Spokesman Alex Mashilo said the gunman targeted Mapaila and was part of a group that booed him when he took to the podium during the commemoration.
"The gunman who was oblivious that there was a video recording capturing his action was among the mob of a few hooligans who were coordinated to boo Mapaila and silence the voice of the communist party. The gunman aborted his mission after what seemed to be an alert to him that he was exposed," said Mashilo.
"In addition, Mapaila had an umbrella because of a heavy rainstorm. This caused a distraction when he ascended the stage where he shortly announced that he could no longer deliver the SACP message because of the storm and quickly exited the podium."
The SACP had previously claimed there was a coordinated plan using state organs to silence those speaking against the African National Congress and President Jacob Zuma's government.
His party, along with alliance partner Congress of SA Trade Unions (Cosatu), have called for Zuma to step down.
Mashilo condemned the actions of the gunman at the commemoration.
"This is a worst form of political and ideological degeneration and will, if allowed to prevail, completely destroy the ANC-headed political movement. In particular this comes against the background of the ongoing systemic murders of SACP members in Inchanga, KwaZulu-Natal.
The SACP will intensify its efforts to tackle the rot politically by democratic means." The party would lay charges with the police, said Mashilo.