The Tánaiste Simon Coveney is reassuring patients there will be no issues with their medication in the event of a no-deal Brexit.
The Irish Pharmacy Union has warned people to keep at least one month's supply of prescribed drugs next March in case the UK crashes out of the EU without a deal.
Work is ongoing to make sure Irish patients have access to vital medicines if there is no deal on Brexit, with the HSE and drugs manufacturers discussing ways to guarantee supplies after the March 29 deadline.
Up to 70% of medicines here come through the UK, and the Tánaiste has said efforts are continuing to guarantee the supply of medicines.
Mr Coveney said: "I'm very confident that the supply of medicines won't be significantly interrupted. There has been a huge amount of work taking place, lead by the HSE.
"The key challenge here is around authorisations and regulations in the UK, because a lot of the drugs that come into Ireland in recent years would have come through the UK, where they would have been authorised by EU bodies, the European Medicines Agency, for example.
"I'm confident that even in a no-deal Brexit the supply of medicines will continue and we already have stock management of medicines in Ireland which means that we have between eight and 12 weeks of medicines in stock in Ireland, which, of course, is a buffer should it be needed as well."