Sandy Row District LOL No 5 organised the parade in support of the Ligoniel lodges and bands, who were prevented from marching their traditional north Belfast route during the summer.
The annual Twelfth of July Ardoyne parade has been marred by serious violence in recent years and restrictions were placed by the Parades' Commission.
A statement released by the Orange Order on Monday night said: "This decision was taken after listening to city centre traders and the local community; and in light of the heightened level of security due to Republican terrorism."
"We believe a further parade at this time through the city centre would not be in the interests of our fellow citizens and therefore as an act of goodwill in this Christmas season we have decided to postpone the parade until early in the New Year."
It is very welcome news and we look forward to a busy trading day on Saturday
Belfast Chamber of Trade and Commerce
The original application had been for 200 people and five bands to march a route from Sandy Row through city centre and on to Woodvale Parade.
It would have taken place on one of the busiest days of Christmas trade.
A statement from the Belfast Chamber of Trade and Commerce welcomed the decision.
The group's president, Paul McMahon, said: "Belfast Chamber of Trade and Commerce has been working with the Orange Order on this issue, we wish to thank them and are delighted that they have come to this decision."
Andrew Irvine of Belfast City Centre Management said: "The news has been warmly welcomed by city centre retailers as they anticipate a buoyant trading day this Saturday.
"We wish to thank the Orange Order for this decision."
Colin Neill, Chief Executive of Pubs of Ulster, said: This is the most crucial time of year for the pubs industry and it needs all the support it can get. We are grateful that the Order have listened to the legitimate concerns of traders and the local community.
Pubs of Ulster warmly welcome the Orange Order's decision to call off this Saturday's parade through Belfast city centre.
Pubs of Ulster
"Pubs in Belfast city centre and indeed across Northern Ireland are very much open for business over the Christmas period and we would encourage people to come out in support of their local pubs and restaurants."
UUP leader Mike Nesbitt welcomed the announcement and hailed the "progressive" actions of the Orange Order in consulting and listening to business owners.
He added: "I understand this is a postponement rather than a cancellation, and while I support the motivation, which is to support the Ligoniel Lodges, I will continue to question the use of the tactic of street protest, which has no record of success in Northern Ireland in terms of bringing about political change. If the end is to see those Lodges complete their 2013 12th of July parade, another means to achieve that end is required, and dialogue is the answer."
Alban Maginness of the SDLP said: "I think it's a very sensible decision. It's good for the people of Belfast and for the traders and for the PSNI.
"They are under pressure given the deadly attacks of last week and can do without the need to engineer a huge policing operation in the centre of Belfast which would have put people off going into the city, disrupted business and destroyed the atmosphere for the people."