Michael O'Neill's side were handed a favourable draw in Group F alongside Greece, Finland, the Faroe Islands, Romania and Hungary after the draw was made in Nice.
The dates for the fixtures have now been revealed and the game against Finland on 29 March next year falls on a Sunday.
It looks set to mark the first time the international side will play at home on the Sabbath, something which has been avoided for religious reasons - however, they have previously played abroad on Sundays.
In the 1982 World Cup, born-again Christian Johnny Jameson ruled himself out of the Northern Ireland game against France because it was on a Sunday.
In 2007 the IFA voted to drop a six decade long ban on Sunday games, however, most teams have continued to honour the boycott.
Ahead of the draw the IFA had agreed to the rules of the competition which included the possibility of a Sunday fixture.
In a change to allowing the respective associations the opportunity to negotiate their own fixtures, UEFA, imposed the dates in order to arrange the best television broadcast deal.
We are part of this group of 54 nations and signed up to this agreement to maximise the opportunity and, fortunately or unfortunately - depending on how you look at it - we have to comply with the conditions established as part of that agreement.
Jim Shaw, IFA president
IFA president Jim Shaw told UTV that the association has no say in the date of the Finland game.
Jim Shaw: "UEFA, as the organising body for this competition, have centralised all marketing for the qualifying rounds.
"This means they are negotiating with the TV people, who are the biggest sponsors of football today, and we don't negotiate anymore and neither do the other 53 countries."
He continued: "The concept they have developed is the week of football.
"The idea is that there will be live competitive international football on Thursday, Friday, Saturday, Sunday, Monday and Tuesday.
"And to accommodate that and meet the requirements of the broadcasters, UEFA set the dates, we don't and that's how we ended up with a scheduled game on a Sunday."
On those people who felt they could not attend a Sunday game, Mr Shaw added: "We respect the individual's own beliefs, but we are in the position we are in."
The IFA chief said a decision on how the tickets would be sold and if the Sunday fixture would be included in the block booking sales, would be made at another date.
Reacting, former Belfast Lord Mayor Jim Rodgers said: "There will be a large crowd at the game - make no mistake - but there will be others who will stay away, or if it's on television, then might just watch it and there could be a protest.
"I have an open mind, but I believe that all of us need a day of rest," the UUP councillor said.
"On the continent they are more accustomed to Sunday games and that might be something we might have to get used to, perhaps if we were this might not be such an issue.
"But it will be up to the individual to make their own personal choice."
This is an attack, I believe, on Christians who, under very sincere and deeply held convictions will feel they either cannot attend the sporting fixture or participate if they have those religious views.
Rev. David McIlveen
Reverend David McIlveen of the Free Presbyterian Church said he had a number of issues with a Sunday fixture.
He told UTV: "This comes under the umbrella of disrespect.
"It is contrary to the teaching of the Bible, wherein we are told to remember the Sabbath day to keep it holy.
"It discriminates against people with those religious convictions."
He added: "Football is played every day of the week and I don't feel there is an appetite for sporting activities on a Sunday in Northern Ireland.
"By observing the Sabbath it gives you peace in your heart because you feel that by honouring God, God graciously honours you."
Rev. McIlveen said he had "no doubt" there would be a protest at the fixture.
He continued: "From a Protestant perspective, I think attendance would be very limited.
"Those who actively support Northern Ireland will be bitterly disappointed they will not be able to go and support on that Sunday in March 2015.
"But I fully expect, they will be outside the ground handing out gospel tracks and seeking to talk to people about how they feel the Sabbath is being desecrated and I will be there with them."
Gary McAllister, of the Amalgamation of the Official Northern Ireland Supporters' Club, said individuals in the Green and White Army should respect each other's beliefs.
He said: "Obviously there will be those that will have an issue with the game happening on a Sunday and fans have in the past encouraged us to ask for no Sunday fixtures.
"Ultimately UEFA has decided and if there are those that want to go, that should be respected equally as to those who decide not to go.
"It is their right to chose to go or not, and equally people can protest but it's important to respect everyone's beliefs."
He added: "I'm very happy with the group, a lot of the teams seem fairly evenly matched and it has the potential to be a very competitive group."
In a statement UEFA ruled out changing the fixture.
"There are no fixture changes possible anymore," the governing body told UTV.
The draw has also thrown up another headache for boss Michael O'Neill as three of the first four fixtures are away.
However, O'Neill said he was pleased with the draw and said there was a chance for qualification.
The qualification campaign kicks off on Sunday, 7 September away to Hungary and ends away to Finland in October 2015.
The Republic, meanwhile, who were drawn against Germany, Poland, Scotland, Georgia and Gibraltar begin their qualification campaign away to Georgia, also on Sunday, 7 September.
Northern Ireland Euro 2016 qualification fixtures:
Hungary v Northern Ireland, Sunday 7 September 2014.
Northern Ireland v Faroe Islands, Saturday 11 October 2014.
Greece v Northern Ireland, Tuesday, 14 October 2014.
Romania v Northern Ireland, Friday 14 November 2014.
Northern Ireland v Finland, Sunday, 29 March 2015.
Northern Ireland v Romania, Saturday 13 June 2015.
Faroe Islands v Northern Ireland, Friday 4 September 2015.
Northern Ireland v Hungary, Monday 7 September 2015.
Northern Ireland v Greece, Thursday 8 October 2015.
Finland v Northern Ireland, Sunday 11 October 2015.
Republic of Ireland fixtures:
Georgia v Republic of Ireland, Sunday 7 September 2014.
Republic of Ireland v Gibraltar, Sunday 11 October 2014.
Germany v Republic of Ireland, Tuesday 14 October 2014.
Scotland v Republic of Ireland, Friday 14 November 2014.
Republic of Ireland v Poland, Sunday 29 March 2015.
Republic of Ireland v Scotland, Saturday 13 June 2015.
Gibraltar v Republic of Ireland, Friday 4 September 2015.
Republic of Ireland v Georgia, Monday 7 September 2015.
Republic of Ireland v Germany, Thursday 8 October 2015.
Poland v Republic of Ireland, Sunday 11 October 2015.