In a letter to DUP colleagues released overnight, party leader Peter Robinson said it would be wrong to proceed with the development because there was no consensus on how the centre would operate.
The First Minister had previously denied claims that the site would be allowed to become a "shrine to terrorists" after objections from other unionist representatives.
He has now retracted his support after "the behaviour of Sinn Féin", claiming that "unionists do not believe Sinn Féin is committed to creating and maintaining this kind of genuinely neutral shared space at the Maze".
Mr Robinson said in the letter that the restriction of the flying of the Union flag from Belfast City Hall in December; the naming of a play park after a deceased IRA member; rising tensions over loyal order parades; and Sinn Féin's support for the IRA commemoration in Castlederg at the weekend were among the reasons for his decision to veto the plans.
"For the centre to be successful in promoting peace and reconciliation, there must be a broad consensus about how it will operate," he added.
"We have consulted widely and it is clear that the necessary wide-ranging consensus does not exist at present. It is my view that it would be wrong to proceed in the absence of a much broader consensus."
The events of recent months - and in particular the insensitive attitude displayed by Sinn Féin towards the innocent victims of IRA terrorism - has seriously damaged community relations and set us all back in terms of promoting genuine reconciliation and building a shared future.
Peter Robinson, DUP leader
The future of the former prison site outside Lisburn has sparked much debate since it was closed 13 years ago.
The jail, which housed many paramilitary prisoners during the Troubles from the 1970s, was closed two years after the Good Friday Agreement.
The project was approved for £18m worth of European funding last year and was given planning permission in April.
Some have been sceptical of the chosen location and have held protests in opposition of preserving the 'H-block' and hospital wing, where the IRA hunger strikers were kept.
Reacting, TUV leader Jim Allister said: "Despite all the diversionary talk from Peter Robinson about the changing stance of others, his Maze u-turn is seismic, but none the less welcome for that.
"The logic of Mr Robinson's analysis of how Sinn Féin is still wedded to justifying terror, leads to the obvious question of why he still sustains them in government?
"Patently, OFMDFM is and will be in disarray over the Maze, which, of course, typifies the paralysis and dysfunctionalism at the heart and top of this failed government."
Commenting on the decision, DUP Lagan Valley MP Jeffrey Donaldson denied that there had been a party u-turn.
"The DUP had sought to find consensus on how the peace centre would operate," he said.
"Clearly that has not been possible, given the recent attitude of Sinn Fein towards the innocent victims of IRA terrorism which has seriously damaged community relations and set us all back in the building of reconciliation."
The party said it was still committed to participating in the all-party talks led by US diplomat Richard Haass in autumn.
People will find it strange that the DUP are now turning their back on such a project and does raise very serious questions about the commitment of elements of the DUP to conflict resolution and peace building.
Raymond McCartney, Sinn Féin
Sinn Féin Foyle MLA Raymond McCartney described the decision as "hysterical," saying that Mr Robinson was being led by Mr Allister and others on the issue.
"He pens a letter telling how he is standing up to the TUV and UUP, yet what he is actually doing is following the agenda they have set for him. It is further evidence of weak political leadership," Mr McCartney said.
"He talks about building a consensus at the same time as he talks up a veto. It is a nonsensical position.
"Peter Robinson, who has himself of course been totally absent over recent weeks, talks about difficulties around issues like parades and emblems. Surely then this should be all more reason why a centre for Peace and Reconciliation should be built."
Ulster Unionist Leader Mike Nesbitt MLA said the decision was a "victory for innocent victims".
He added: "As to Mr Robinson's ridiculous attempts to blame the Ulster Unionists, we will say nothing unless and until he acknowledges the role played at that time by his DUP colleague Edwin Poots - both as a member of the Maze panel and as a Lisburn Councillor.
"Mr Robinson also fails to explain why he did not address what he clearly feels was a mess during the St Andrews negotiations."
SDLP leader Alasdair McDonnell said the First Minister's move was "another example of DUP lack of leadership".
"Mere months ago, Peter Robinson described the suggestion that the H-blocks jail and peace centre could become a shrine to terrorism as 'scaremongering garbage'," he commented.
"Now in a complete u-turn, he says it would be wrong to proceed and blames Sinn Féin's attitude to victims. In his justification for this u-turn, the DUP's attitude to victims - like Sinn Féin's - has been brought into sharp focus and has yet again proven to be hypocritical and damaging to their credibility."
Mr McDonnell stressed the importance of engagement at the upcoming Haass talks in moving forward.
"It is evident that the political process has been soured by DUP actions. We are walking ourselves into a political crisis, but there is an opportunity to turn this situation around," he said.
Alliance Party MLA Trevor Lunn said: "This letter from Peter Robinson has profound consequences for the Haass talks, due to start next month.
"Rather than relying solely on Richard Haass, the onus is on all Parties to work together to reach the best way forward for Northern Ireland, rather than letting the desire for votes drive their actions."
Meanwhile, the Grand Orange Lodge of Ireland has welcomed the DUP decision.
Deputy Grand Master Rev Alistair Smyth said: "The Grand Orange Lodge of Ireland has always maintained that the development of a so-called peace centre at the site of the former Maze Prison would serve to only deepen the trauma and prolong the healing process of the innocent victims of terrorism."
Progressive Unionist Party leader Billy Hutchinson has welcomed the First Minister remarks, describing them as "a positive step."
He added: "The PUP has been the only party to hold a consistent position on the Maze site and our opinion remains that it should be razed to the ground."