The company, which opened a branch there in 2017, says the location was loss-making.
The firm also has outlets in Exchequer Street and Dun Laoghaire, both of which it says will be unaffected by this closure.
The company recently signed a 25-year lease on its flagship Exchequer Street building.
The Rathmines store was based in The Swan Shopping Centre.
A note about Fallon & Byrne Rathmines pic.twitter.com/HMomQPBtmJ
— Fallon and Byrne (@FallonandByrne) January 2, 2020
In a statement the company said:
"Unfortunately the location was loss-making and, while the decision was a very difficult one, we believe that acting decisively is what's best for the business overall".
It says management "will be re-focusing" on its Exchequer Street outlet.
The company also thanked its team, suppliers and customers for their "ongoing support."
