The SACP believes there was a gunman at the Chris Hani commemoration on Monday who threatened the first deputy general secretary of the party, Solly Mapaila.
"They wanted to repeat what they did with comrade Chris Hani, with Comrade Solly," said SACP spokesperson Alex Mashilo.
The party has referenced a News24 video to support their claims.
In the video, a man in the marquee can be seen holding what the party believes is a gun. He is among a crowd of people that booed Mapaila when he took to the stage at the Thomas Nkobi cemetery, where Hani is buried.
Standing a few metres from the podium, the man is seen wielding the item and then putting it down while Mapaila was trying to address the crowd.
Mapaila was not able to deliver his commemorative message as a thunderstorm broke out.
Police told News24 that they were not aware of the incident.
Mapaila has led calls by the ANC tripartite partners for President Jacob Zuma to step down following his decision to reshuffle his Cabinet, firing five ministers, including finance minister Pravin Gordhan, without consulting the partners.
The SACP says those threatening Mapaila must know that he is not acting as an individual, but carrying out the mandate of the party collective.
It has also blamed the alleged incident on the factional battles plaguing the ANC.
"These thugs wanted to commit 10 April the second time on the graveside of Comrade Chris Hani. They are shameless and rotten to the bone marrow in pursuit of the factionalism that is destroying our liberation movement and now wreaking crisis through corruption, corporate capture and spying on comrades," Mashilo said.
The SACP condemned the incident, and said it would take action, legally and politically.
Ekurhuleni Mayor Mzwandile Masina told journalists that the rainstorm stopped the programme of the day, but did acknowledge there were some rogue elements in the crowd, which he said did not belong in the region but were bussed in to cause disruptions.
Mapaila was first booed when his name was called out for him to go lay a wreath on Hani's grave on behalf of the SACP.
Hani was the general secretary of the SACP at the time of his shooting.
The event also saw the breaking of the usual protocol of having a keynote speaker address the crowds last, as Zuma spoke before the messages of support from the alliance partners, and left immediately after addressing the crowd.
Mashilo said the party was yet to take the complaint to the police, but it had information about the gun incident that it was not at liberty to share yet. He also said the SACP would discuss the incident and other related matters with the ANC.
"We didn't communicate with them. Mzwandile [Masina] shared the information with comrade Solly about the people who were bussed in - coming from outside Ekurhuleni," he said.
Mashilo said the process the party was undertaking would include criminal processes.