Five of the blocks were to be brought down at the start of the Games in July.
The plan proved controversial, with an online petition against the demolition gathering more than 17,000 signatures.
Glasgow 2014 said opinions being expressed about "safety and security" meant the destruction of the flats would not now feature in the opening.
Continue reading the main storyOpinions have been expressed which change the safety and security context”End Quote David Grevemberg Glasgow 2014 chief executive The 30-storey structures were built in the mid 1960s and the original eight tower blocks housed more than 4,000 people. The demolitions will now be rescheduled.
Risk fears
Opponents had questioned the message the demolition would send and described the plans as insensitive to former residents as well as asylum seekers currently living in the sixth block.
In a statement, Games chief executive David Grevemberg said: "We made it clear from the outset the absolute priority was safety and that this event would only happen during the opening ceremony if it was safe to do so.
"Over the past few days it has become clear that opinions have been expressed which change the safety and security context.
"Glasgow 2014, Games partners and key stakeholders, including Police Scotland and Glasgow Housing Association, are not prepared to allow what was proposed to be a positive act of commemoration to create risk for all concerned, including the communities of north east Glasgow."
'Dignity' callFormer Scottish Socialist MSP Carolyn Leckie, who launched the petition, had been due to meet with Glasgow 2014 representatives to discuss the plan on Tuesday.
The petition called for the flats to be brought down with "dignity" and not as part of an entertainment spectacle.
The event was to have be shown live on a massive screen at the Celtic Park ceremony and to a huge TV audience.
Glasgow 2014 said the demolition was a matter for Glasgow Housing Association (GHA) and would take place as part of their ongoing regeneration programme.
However, Mr Grevemberg said Glasgow 2014 would still dedicate an element of the opening to telling the story of Glasgow's social history.
A GHA spokesman said: "As we have stated all along, public safety is our absolute priority. The demolitions will be rescheduled and we will continue to liaise and take the advice of the police and our demolition contractor."
A Glasgow City Council spokesman said: "We support the organising committee's decision. Public safety must always be paramount on these occasions."
Monday marks 100 days until the start of the Games.