At a hearing at Tehran's Revolutionary Court on 9 August, both women refused orders to recant their faith and were sent back to prison.
Christian Solidarity Worldwide is supporting the vigil, organised by Iranian Christian women in the UK who will dress in white for the occasion.
It says that neither woman has committed a crime under Iranian or international law and believes that their health is rapidly deteriorating because of the overcrowded conditions and limited facilities in the prison.
Iranian apostates - Muslims who convert to another religion - often face arbitrary arrest, indefinite detention and other human rights abuses, says CSW.
Mervyn Thomas, Chief Executive of CSW said: “We wholeheartedly stand in solidarity with Maryam and Marzieh, who are being held solely on the basis of exercising their most basic right: freedom of thought, conscience and belief.
"Scores of illegal detentions of Christian converts in Iran have been reported this year, and we strongly urge the Iranian Government to release these innocent women immediately."
