Last month Zambian authorities charged Hichilema, of the UNDP, with treason for obstructing Zambia President Edgar Lungu's presidential motorcade.
If found guilty, Hichilema faces a 15-year jail term, or possibly even the death sentence.
On Friday, Zambian authorities refused Democratic Alliance (DA) leader Mmusi Maimane entry into Zambia, where he had intended to attend the treason trial of Hichilema.
The DA leader was sent back to SA at the Lusaka International Airport without being allowed to disembark from the plane.
Numsa General secretary Irvin Jim on Tuesday said: "On our part as a working class formation, we will do what we must, to stop the slide into civil war in Zambia, as a result of the dictatorship of President Lungu."
He added: "We stand in solidarity with ordinary Zambians who are fighting for freedom and for the right to live in a country free of fear and state-sanctioned brutality. One of the greatest tools of the resistance in South Africa was organised labour.
"It was members of the working class who stood up and fought back against an inhumane and oppressive racist state. If Zambia is to be free then workers must unite and act with courage to resist all forms of oppression.
"Furthermore we call on all our global partners to express solidarity with our brothers and sisters on the continent as they battle for a free and just society."
Numsa said Zambia under President Lungu, was a "confirmed dictatorship", and as a union Numsa "will condemn tyranny in all its forms and wherever it raises its ugly head".
"This is why we have been consistent in condemning the repressive administration, of Zambia President Lungu. We have consistently warned the world about the slide into authoritarianism and dictatorship in Zambia," Jim said.
He warned that Zambia was "on the brink of civil war" unless it resolved its political crisis.
"As far back as March this year, Numsa highlighted that the Zambian government had declined into a tyrannical state, and was systematically silencing opposition voices of any kind. The first sign of an autocratic regime is one that bullies and harasses members of the press," said Jim.
"It launched a vicious campaign against independent media houses like the The Post newspaper, and even succeeded in having the paper shut down. Other media houses like Muvi TV, and Komboni Radio were also victims of harassment when the state temporarily suspended their broadcasting licenses.
"Numsa reiterates its call for a boycott campaign of all Zambian products to highlight the suffering of ordinary people there. South Africa owes the people of Zambia a huge debt, we dare not fail them in their time of great need. We must do all we can to end the totalitarian regime of Lungu and his cronies before it's too late."