The Save SA protest is one of many planned against Zuma across the country.
"We issue a clear and unambiguous message to our members to not join this march and not participate in any activities organised by Save SA," the trade union federation said on Thursday ahead of the march planned for Friday.
"We are not confused about who our enemies are and in everything we do, we will be guided by our class interests, we will never march with the agents on monopoly capital to remove a democratically elected government."
The federation said it would not allow itself to be used by those who were pushing for "regime change" agenda.
"Cosatu is clear that as the [tripartite] alliance, we need to wage a robust struggle against our own weaknesses including self criticism, but we will never sell out to the agents on white monopoly capital and their stooges. The ruling African National Congress, Cosatu and the South African Communist party form the tripartite alliance.
"The fact that some people agree with us on the President stepping down, does not mean that they are our friends. They are saying this to drive their narrow regime change agenda and we reject it," Cosatu said.