AIB has said ATMs will also be removed from these branches.
AIB will make 70 of its 170 branches cashless this autumn, as it claims demand for cash services has dropped and the cost of security has risen.
This includes the branches in Celbridge, Athy and Edenderry.
The bank has said the move will allow it to focus on other priorities, including mortgages, loans and investments.
The cashless banks will come into operation on September 30th and October 21st, and AIB say ATMs will also be removed from these branches.
It will broaden cash and cheque services for customers at 25 Kildare post offices, with An Post’s Saturday service and longer opening hours.
AIB customers can lodge up to €5,000 a week and withdraw €1,500 in cash a day from their bank account at any post office.
The decision by AIB to change seventy fully functioning retail Bank branches to cashless branches has been sharply criticised by the Financial Services Union (FSU.
John O’Connell, General Secretary of the FSU commented: “The banking sector is currently struggling to navigate through the withdrawal of two retail Banks from the market.
"Over a million customers will have to open new accounts and close their current accounts. How can a state-owned Bank think this is a suitable time to withdraw banking services from communities across the Country?
"We are in the middle of a banking review set up by the Minister for Finance with access to cash an issue that is under consideration.
"The announcement today shows a complete disregard by AIB for this process and reflects a growing disconnect between the value placed by the Banks on the requirements of stakeholders compared to the requirements of shareholders.
"We have survey after survey showing trust levels in the banking sector at an incredibly low level.
"The announcement today will only validate the view that the main retail Banks in Ireland do not value their customers or staff and are mainly focused on ensuring their shareholders are paid hundreds of millions of euros in dividends," he insisted.
"We will be left with no functioning retail banking network unless there is real change in the way the banking sector is regulated. We need to ask If there were workers directors on the board of AIB today would this decision have been made.
"The regulator and the Government should inform AIB not to proceed with this proposal until the banking review is complete and the issues around the withdrawal of KBC and Ulster Bank has been resolved," he added.
Public Affairs Manager at An Post, Angus Laverty, has further details of the update: