A New Zealand Post spokeswoman said the Tarbert St premises would shut its doors on Wednesday, February 28.
The postbox lobby in the building would remain.
Paper Plus, at 64 Centennial Ave, would become the NZ Post and Kiwibank agent from March 1.
Customers in Alexandra would be able to post letters and parcels, buy postage and access over-the-counter banking services from Paper Plus.
The spokeswoman could not confirm what would be done with the Tarbert St site, but said NZ Post was "looking at opportunities" for the space.
The four permanent staff and one casual staff member who worked at the store were employed by Kiwibank.
A Kiwibank spokeswoman said Kiwibank was unable to provide local redeployment options and individual agreements were reached with all of the staff.
NZ Post announced the closure in September but did not have a closure date at the time.
