The South African Communist Party (SACP) has been increasingly critical of Zuma's corruption-tainted leadership, which has seen the ANC suffer a sharp drop in public support.
It will be the first time that Zuma, who came to power in 2009, has not addressed the congress, held every four years.
"We advised the ANC that due to the tensions we are having... It would be best for the president not to address the national congress," party spokeswoman Hlengiwe Nkonyane told AFP.
The party has called on Zuma to step down following mounting allegations against him, including over the wealthy Gupta business family, which is said to have undue influence over his government.
The SACP, along with the ANC and the trade union federation COSATU, was at the forefront of the struggle to end white-minority rule that led to the first non-racial elections in 1994.
On August 8, Zuma will face a motion of no-confidence in parliament called by the opposition.
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