The company employs 690 people, 190 of them full-time, in those two stores and in Cork, Galway, Liffey Valley, Limerick, Naas, Swords and Tallaght.
The company believes seven stores could be viable if rents are cut and other cost-cutting measures implemented. It is paying €11.6m rent for the stores, about €5.8m above open market rents.
All vouchers, credit notes and deposits will be honoured by the company throughout the examinership period.
Rossa Fanning, for the company, said B&Q Ireland was insolvent with liabilities of more than €17m to its parent company, Kingfisher, but has no bank or revenue debts.
Its turnover had fallen 24.2pc from a peak of €124m in 2009 to some €94.2m in the financial year to end January 2012.
A loss of €20.5m is forecast for the year ended January 2013, including restructuring.
Kingfisher had written to the company saying the business was not sustainable with its current cost base.
Kingfisher had also indicated it would provide financial support to the company if it was under court protection.
Mr Justice Peter Kelly appointed Declan McDonald of PWC as interim examiner.