The Mullingar store and six others were described as 'unviable' in a statement released by boss James Byrne.
The 12 staff at the store at Lakepoint in Mullingar will lose their jobs at the end of March and the store is currently running a closing down sale.
The statement said: "We would like to thank our staff for their tremendous efforts and support and we deeply regret the impact of this closure on our staff in Mullingar."
Byrne declined to comment on the total number of staff to lose their jobs.
The Byrne's chain began with a shop in Wexford over 29 years ago and expanded until 2007 when it had 19 outlets across Ireland.