Robin Swann advised the Executive on Monday night that a travel ban could have "serious adverse implications" on the financial viability of aircraft and ferry routes, leading to a knock-on effect on the supply chain of essential goods and services.
The Health Minister said that while there was merit in a Great Britain travel ban, travellers entering Northern Ireland from the Republic of Ireland posed a greater risk than travellers entering Northern Ireland from the rest of the UK.
The details were contained in a paper, seen by the Belfast Telegraph, that Mr Swann presented to the Executive.
The Executive voted against imposing a travel ban on Great Britain late on Monday after a mutant strain of the virus was identified in parts of the UK.
Mr Swann said it was probable, but not confirmed, that the new strain had already arrived in Northern Ireland and the Republic, with rising case numbers south of the border likely down to the new variant.
Sinn Fein and the SDLP backed a ban, but Alliance, the DUP and UUP voted against.
Plans to issue new guidance against all but essential travel between Northern Ireland, Great Britain and the Republic were unanimously backed.
Mr Swann said this should include people wishing to return home for the holidays.
The paper presented by the Health Minister advised that banning travel could cut supply lines, which even on a temporary basis could mean "significant costs" for the Executive.
Although the presence of a new coronavirus strain, which Health Secretary Matt Hancock said over the weekend was "out of control" in England, has not been confirmed in Northern Ireland, Mr Swann said the benefit of banning travel would be "somewhat reduced" if it was already present here.
Advice from the Chief Medical Officer Dr Michael McBride and Chief Scientific Adviser Ian Young told the Executive the "relative risk" for travellers from Great Britain having Covid-19 was less than one in 100 and at rates "significantly less" for the new variant.
But the advice said there was merit in taking a precautionary approach in the absence of concrete evidence the new strain is present. Limiting travel from the Republic of Ireland, given the "current disease trajectory," was also suggested.
"Given the extent of traffic between RoI and the UK, it is almost inevitable that the variant is present in RoI where it is unlikely to be easily detected given that little sequencing is performed," the paper said.
Travel-associated cases of Covid in Northern Ireland currently represent a comparatively small number of all cases.
Of 6,000 new cases reported over the past two weeks, only 23 people reported travelling to the rest of the UK.
"More cases report having been in RoI in the same period," the paper said.