The parade was due to pass the scene of a sectarian attack on a priest during a similar event that was held on 7 July.
Police Scotland are investigating claims Canon Tom White was spat on as an Orange parade passed St Alphonsus church in the city’s east end.
Glasgow City Council confirmed the walk would not go ahead following a meeting with the organisers.
The Orange Lodge said the postponement would allow time for further discussions.
Police were called after reports Canon Tom White was spat on, struck with a baton and verbally abused outside the church, near the Barras market, as the parade passed by.
In a statement on Facebook, the Archdiocese of Glasgow said that both Canon White and his parishioners had been “subjected to vile abuse”.
Orange Lodge leaders insisted that the attack was nothing to do with the parade and none of its members was responsible.
The ordeal sparked calls for a ban on Orange walks or a change of route away from the Catholic church involved in the incident.
Council leader Susan Aitken ordered Orange Lodge leaders to take responsibility for anti-Catholic behaviour occurring at their parades and warned organisers that if it did not voluntarily change the route of parades, the council would “insist”.
A meeting took place between the council and the Grand Orange Lodge of Scotland on Wednesday.
Following discussions, a council spokeswoman said: “Council officers had a productive meeting with the organisers.
“We will continue to engage with both the organisers and the church community - but have agreed that the planned procession will not take place on Saturday.”
A spokesman from the Grand Orange Lodge of Scotland said: “We welcome the opportunity to continue positive dialogue with Glasgow City Council, the police, and other stakeholders regarding future parades.
“We should be looking forward, not back, and our lodges therefore took the decision to postpone the parade due to take place this Saturday, therefore allowing some additional time over those discussions which would give everyone the opportunity to look at matters from a fresh, forward thinking perspective.
“The Grand Orange Lodge of Scotland fully supports this decision.”
Police Scotland continue to investigate the attack on Canon White.