Following a warning from the Association of British Insurers (ABI) last month that anyone driving across the border after March 29 could be breaking the law, insurance providers have begun issuing customers with the documents.
The green cards are international certificates of insurance that prove UK firms will provide minimal compulsory cover for their customers while driving in the Republic.
All UK drivers planning to travel to any EU country will be required to carry the document should Britain leave the EU without a deal at the end of this month.
A deal between UK and EU authorities was agreed in May 2018 to waive the requirement but has yet to be ratified by the European Commission.
Motorists in the south are also being provided with the documents by the Motor Insurers’ Bureau of Ireland for cover in the UK.
Among the UK firms issuing the cards is Admiral, which has now contacted customers with advice.
It said: “As you are a resident of Northern Ireland, we will be sending you a Green Card by post in due course.
“In the event of a no-deal Brexit it may become necessary for residents of Northern Ireland to have a Green Card when travelling to the Republic of Ireland.
“You will still have the same level of cover you enjoy in the United Kingdom but may need to show the Green Card when crossing the border.”