The branch has been under investigation since June
Joint provisional liquidators have been appointed to Rush Credit Union.
Jim Luby and Tom Rogers of McStay Luby were appointed as joint provisional liquidators by Mr Justice Peter Kelly at the High Court.
A full hearing will take place in around two weeks, and the Central Bank will seek the winding up of the credit union.
The appointment does not have any impact on members’ savings in any other credit union.
For customers of Rush Credit Union, the Central Bank says the Deposit Guarantee Scheme (DGS) has been activated - meaning payments will automatically issue to addresses held on file by the credit union.
In a statement, the Central Bank said: "The Central Bank believes it is necessary to apply for the winding up having regard to the concerns which it has relating to certain governance and financial issues faced by Rush Credit Union, some of which are already in the public domain.
"In the absence of taking the proposed action, the nature of the financial, governance and internal controls issues, could lead to a disorderly collapse of Rush Credit Union," it adds.
Investigations have been ongoing in the credit union since June, after financial irregularities were highlighted when €700,000 went missing from accounts at the branch covering Rush and Lusk.
The Central Bank, which carried out the initial investigation, has moved to reassure the branch's 10,000 customers that their savings will not be affected.
"Members' savings are covered by the statutory Deposit Guarantee Scheme up to €100,000 per member," they said in a statement.
Fine Gael TD for Dublin Fingal, Alan Farrell said the decision by the Central Bank to liquidate the credit union is “shocking for members and a major cause of concern for staff”.
“Over recent months, we have heard a great deal in relation to the reported irregularities in record keeping in Rush and Lusk Credit Union. These reports have caused much concern for both residents in the local community and customers of the credit union.
The need for these irregularities to be accounted for is not negated by the decision of the Central Bank to liquidate Rush and Lusk Credit Union. The reports undoubtedly compromised the integrity of this local service and all members of the credit union deserve to know exactly what happened within the credit union in relation to these reported anomalies."
The initial figure of €700,00 is thought to have doubled, according to reports in the Irish Independent. The cost to stabilise the union is thought to exceed €5 million.
Last month, the Central Bank obtained a High Court order extending the suspension of credit union manager, Anne Butterly, from holding a management position in a financial services firm.
Acting chairman Gerry Foley has resigned citing personal circumstances.
No-one has been charged in relation to the irregularities at the credit union.