In a statement on Friday, the Special EU Programmes Body said it has rescinded its offer of finance following discussions on the viability of the project.
"It has been agreed that the project is no longer viable at this time and the SEUPB has therefore rescinded the letter of offer," the statement said.
"The SEUPB will now consider the re-allocation of funding to suitable projects."
European Commissioner for regional Policy Johannes Hahn added: "This is a project which we supported as a contribution to the reconciliation of the communities in Northern Ireland. Sadly due to to the political conditions on the ground, we cannot go ahead in this period."
"I very much hope that we can try again with this project and that for the time being the money from it can be used to fund other projects."
The £18m funding was approved last year following backing by the NI Executive.
The announcement comes after First Minister Peter Robinson withdrew its support to build the facility in August over fears it would become a "shrine to terrorists".
The party accused senior Sinn Féin member Gerry Kelly of celebrating terrorism at a republican commemoration this summer.
The former prison site outside Lisburn has sparked much debate since it was closed 13 years ago in the wake of the Good Friday Agreement. The former 'H-block' and hospital wing housed IRA hunger strikers in the 1980s.
While the offer of EU funding for the Maze prison site has been removed, Sinn Féin insists the Maze project has not been shelved.
The redevelopment of the former prison site formed part of the Programme for Government agreed by Martin McGuinness and Mr Robinson.
Mr McGuinness said the unionist u-turn came following weeks of violence on the streets over parades and flag protests.
"Very strenuous efforts will be made over the course of the coming period to bring people to their senses and to recognise that we cannot kowtow to those violent elements on the streets, who are at the heart of overturning this project", he told UTV on Friday.
The deputy First Minister added: "I have stood four-square against those on the so-called republican side who wish to bring the institutions down and disrupt the work of government. Others have to do the same."
Today's development further underlines there will be no immediate development at the Maze Prison site. It also feeds further into concerns about the political situation here and the lack of agreement on a number of issues.
UTV's Marc Mallett
The money is only available until 2015 and the race is now on to find other viable projects in the region.
DUP MEP Diane Dodds said she welcomed the desire for the money to stay in Northern Ireland.
"I have spoken to SEUPB Chief Executive Pat Colgan over recent weeks and again today to highlight some of the projects that can be delivered within the timeframe available," she said.
"One such project, the Valley Park Shared Space Project in Newtownabbey, is ready to be rolled out and has been previously approved for funding by SEUPB.
"As MEP, I work alongside many groups who have great ideas but simply cannot access funds. These funds represent a real opportunity and over the coming days I will be continuing to lobby SEUPB to ensure this money is used to the maximum community benefit."
Fermanagh and South Tyrone UUP MLA Tom Elliott says the money can be "reallocated to other much more worthy and less contentious projects".
"The focus must also be on ensuring that the Maze site is still regenerated to create up to 5,000 jobs as was originally envisaged," he said.
Alliance Lagan Valley MLA Trevor Lunn said that the DUP leader and his party should be blamed for the withdrawal of financial support.
"It was a cowardly move by Peter Robinson to make this u-turn while he was in America," he said.
"This example of weak leadership has now resulted in a major development opportunity being lost that would have created a large number of jobs and been a big boost to our struggling construction sector," he added.
SDLP MLA for Mid-Ulster Patsy McGlone has hit out at Sinn Féin and the DUP.
He said: "OFMdFM have squandered the crucial funding available for completion of the Maze Peace Centre and in doing so has serious questions to answer to those in the construction and tourism industry."
John Armstrong, Managing Director of the Construction Employers Federation, said the announcement was a "major disappointment for the local construction industry".