Protesters are due to gather this Sunday at 2pm by the plaque on the road, in Crookes, where the trees were planted in tribute to former Westways Primary School children killed during the First World War.
Cabinet members voted on Tuesday to fell 23 of the trees on that road, which are said to be dead, diseased, dying, damaging property or obstructing the road or pavement.
They said they could not justify spending the £500,000 council contractor Amey estimated it would cost to save the trees, but they promised to replace the trees and to plant around 300 new war memorial trees in the city's parks.
Campaigners fighting to save the trees questioned the figure quoted, insisting the work could be done more cheaply. They criticised the council for failing to get an alternative estimate.
The Last Post will be played at Sunday's vigil, followed by a minute's silence and speeches.
Laura Gordon, the Liberal Democrat parliamentary campaigner for Sheffield Hallam, is one of the organisers of Sunday's vigil.
She called on the council to explain how the £500,000 figure was calculated, adding: "Sheffield, and its history, deserves better – the memorial trees need to be and can be saved."