Ulster Bank and KBC current account holders need to switch banks now, so they don't get a cheque with their remaining balance in the post.
The Competition and Consumer Protection Commission is making the appeal after it emerged that less than half of affected customers have opened new accounts to date.
A service has been set up by the CCPC to help current account holders make the switch, ahead of the banks exiting the market.
It includes a step-by-step guide to transferring direct debits.
Grainne Griffin, Director of Communication with the CCPC, says people shouldn't be left out of pocket when they move.
"KBC has announced that they will waive fees for consumers once they're informed their account is closing.
"Ulster Bank hasn't made the same move yet, although we're hopeful that they will in the future - it's certainly in consumers' best interests.
"The main message we're saying to consumers is you shouldn't be out of pocket because of these changes, and if you are, that's an issue you should raise with your bank.
"You don't want to reach the closure point at some point next year, realise you didn't do anything about it and receive a cheque with your remaining balance in the post.
"From what we've seen in our research, people are aware that they need to switch current accounts, it's simply a case of taking those steps sooner rather than later to make sure you're all set."
Darragh Cassidy, Head of Communications at Bonkers.ie, is encouraging people to switch as soon as possible.
"Time is ticking. You absolutely want to ensure that you're not left in the situation where you've no bank account, where you don't have access to money, where direct debits and standing orders are bouncing.
"Look at switching now - choose a new provider as quickly as possible."