The warning comes as Northern Ireland’s health service battles one of the worst outbreaks of Covid-19 in the UK.
The vast majority of the medicines used in Northern Ireland are imported either from or through the rest of the UK, often from the European Union.
But members of a House of Lords committee told health minister Edward Argar they fear supplies will be disrupted because of new checks, due to be introduced when the Brexit transition period finishes at the end of December.
They have demanded answers on a series of questions, including stockpiling levels and any other steps ministers have taken to ensure people in Northern Ireland can still access much needed prescriptions in January.
The Northern Irish health system is currently under extreme pressure, with a number of hospitals warning they have patients for whom they are struggling to find beds.
There are fears disruption to vital medication on top of a large number of coronavirus cases would only make the crisis worse.
Lord Teverson, the chair of the committee, has written to Mr Argar asking for reassurances.
"What steps is the Government taking to ensure the consistent, affordable supply of a full range of genuine prescription medicines in NI in the medium term, after any immediate adjustment period at the end of transition?" he wrote.
The peer has given the minister until November 11 to respond.
Earlier this week consumers were warned the price of the weekly shop would rise considerably in the event of a no-deal Brexit.