"During the early hours of this morning [Saturday], people came and petrol bombed the marquees, stage, sound system and chairs," said EFF spokesperson Mbuyiseni Ndlozi.
"No arrests have been made, but we have opened a case with police."
The party's premier candidate Dali Mpofu was due to address the rally at the Sam Ntuli stadium at 10am.
Ndlozi said the event will still go ahead.
"The event will still go on but at 2pm. Dali will speak."
He said police were monitoring the area and a helicopter was hovering above.
"We are not going to back down, we will stand our ground and continue with event."
'Threats of disruption'
He said it suspected that ANC members could have been behind the arson attack.
"Police and the EFF were tipped off [on Friday] about threats of disruption by ANC members [but] we thought the disruption would happen during the event."
ANC spokesperson Jackson Mthembu rejected the accusation.
"We never do such things. This is an unfair accusation," he said.
"It is totally uncalled-for and anyone who burnt that marquee must be found and prosecuted."
He said the EFF's accusation amounted to negative politicking, which went against the Electoral Act.
Mthembu said the flood gates for negative political practises ahead of the elections have been opened following the ruling by the North Gauteng High Court in Johannesburg relating to an sms by the Democratic Alliance.
"People have a license now to say anything about a political party. This is what we feared," he said.
The ANC's application was for the DA to retract a text message sent to more than a million potential voters accusing President Jacob Zuma of stealing public money. This follows the release of the public protector's report into upgrades at Zuma's Nkandla homestead.
Judge Mike Hellens dismissed the ANC's application with costs, finding that the sms constituted "fair comment".
Mthembu said that Hellens failed to take aspects of the Electoral Act into account in his judgment. – Sapa