Since the 1920s the UK and Ireland have operated a Common Travel Area (CTA) which allows nationals of both countries to travel and live in each country without immigration controls.
They are part of an EU customs union which means there are no controls on goods.
The Northern Ireland Office (NIO) said: “Without this, goods being exported across the border could be subject to various forms of customs controls and their liability to duty determined according to complex rules of origin.”
The department wrote to the Northern Ireland Affairs Committee of MPs and said it was important to business and communities that the border remains fully open.
“The absence of cross-border restrictions has both encouraged cooperation and increased trade over the last 20 years.”
Overall, around 60% of Northern Ireland’s exports go to the EU, with 37% going to Ireland alone.
The statement said: “If the UK left the EU, these arrangements could be put at risk.
“Questions would also need to be answered about how the Common Travel Area, which covers the movement of people, would operate with the UK outside the EU, and Ireland inside.”
The Democratic Unionists are campaigning for an exit and have sought to downplay the prospect of security checks on the border, pointing out that it is already covered by an elaborate electronic surveillance system.
The Remain campaign has raised concerns about the impact of an EU withdrawal for free movement between Northern Ireland and the Republic of Ireland.
Northern Ireland Secretary Theresa Villiers favours an exit but the Government as a whole is campaigning to remain.
Ireland’s establishment has voiced concern about the impact of a Brexit on Anglo-Irish relations.