A fatal foetal abnormality diagnosis means doctors believe an unborn child has a terminal condition and will die in the womb or shortly after birth.
The proposal to allow abortion in such cases was defeated by 59 votes to 40.
The result followed a passionate debate at Stormont after some MLAs proposed the law change be introduced by way of an amendment to the Justice Bill.
Unlike other parts of the UK, the 1967 Abortion Act does not extend to Northern Ireland.
Currently, a termination is only permitted in Northern Ireland if a woman's life is at risk or if there is a risk of permanent and serious damage to her mental or physical health.
Politicians have been lobbied to reform the law since 2013, when Northern Ireland woman Sarah Ewart spoke out about having to travel to Great Britain for an abortion after she was told she was carrying a baby that had no chance of survival.
The Democratic Unionist Party (DUP) faced criticism from other parties during Wednesday's debate for asking the Health Minister Simon Hamilton to set up a working group to examine the issues raised by fatal foetal abnormality.
It could take six months for the group to complete its work and the Ulster Unionist leader Mike Nesbitt claimed it was a DUP "device" to delay decision making on abortion reform until after May's assembly election.
Justice Minister David Ford, who brought forward the proposed change to the legislation, told Radio Ulster's The Nolan Show it could now remain in limbo for some time.
"It would appear that that is what some people want, that it was any excuse at all to avoid taking a decision last night so they can fudge the issue," he said.
"We will wait and see what happens to the DUP's supposed working group for the next six months. Certainly, we'll get the DUP past the election, maybe that's why they're doing it."
However, the DUP has argued that the issue required proper consideration by MLAs and ministers and that the Justice Bill was not intended for this purpose.
The amendment to legalise abortion in cases of fatal foetal abnormality was proposed by Alliance MLA Stewart Dickson.
He told MLAs: "If we are to continue to fail women in Northern Ireland in this area then we are abdicating our duties as representatives.
"The traumatic journey to England for many young women is becoming a shame on Northern Ireland and to force women with a fatal foetal pregnancy to look elsewhere for help and support make this worse."
The amendment relating to pregnancies which are the result of rape or incest was put forward by Anna Lo, also of the Alliance Party, and was defeated by by 64 votes to 30.
Mr Nesbitt said that as a man he did not feel comfortable "discussing what a woman should do with her body" but he added that MLAs had a responsibility to legislate.
He claimed the DUP's request for a commission was a delaying tactic designed to "kick the decision to the far side of the election".
Mr Nesbitt described the delay as "cruel" and "Dickensian".
"This is Bleak House we're in today, in the Chancery courts waiting day after day, after day, after day for a decision that never comes," he said.
Sinn Féin MLA Caitríona Ruane also criticised the DUP for "supporting a commission which will report in six months".
"What about the plight of women in the here and now? What about the women who are pregnant as the result of rape, or women who are faced with fatal foetal abnormalities?
"Is the DUP going to tell them 'we're having a commission in six months and sure, then we'll see where is goes?'  I'm sorry, long-fingering this does a disservice to women," Ms Ruane said.
However, Social Democratic and Labour Party (SDLP) MLAs expressed doubt that doctors could accurately predict that an unborn child had no chance of survival.
SDLP MLA Dolores Kelly said clinicians had told her party that "there is no such definition" as fatal foetal abnormality.
Speaking independently from her party, Alliance MLA Anna Lo proposed that women who have become pregnant as a result of sexual crime should have access to a legal abortion in Northern Ireland.
Ms Lo said that forcing pregnant rape victims to give birth meant they would be "reminded every day of that act of violence which was forced upon her".
However, Traditional Unionist Voice (TUV) leader Jim Allister described Ms Lo's amendment as a  "charter for abortion on demand".
He said that because of his background as a barrister he had more experience than most MLAs of rape trials and added that "95% of the time, the question for the jury is - was the sexual intercourse consensual or not?"
"All you have to do is to allege indecent assault it seems, rape, and you're entitled on the nod of a medical practitioner to abortion," he said.
Mr Allister told MLAs that allegations of rape could only be proven through "due process" and this was not possible within the timeframe of pregnancy.
DUP MLA Emma Pengelly spoke in support of the working group on fatal foetal abnormality.
"I have not had the beautiful privilege to have brought a child into this world but I can empathise with all my heart that the wished for, the longed for, can turn so quickly to tragedy," she said.
"The way forward that we are proposing is a compassionate one, it is a sensible one, it is a common sense one that will leave all of us in a much better and informed position to chart a loving and kind way forward."
At the end of the debate, Assembly Speaker Mitchel McLaughlin commended MLAs on the "sense of dignity" they displayed during the discussions.
Stormont's chief legal adviser, Attorney General John Larkin QC, is among those who are opposed to changing the law and has outlined concerns that the move could breach obligations under the United Nations Convention on the Rights of Persons with Disabilities (UNCRPD).
Precious Life, one of the largest pro life organisations in the region vowed to "expose" any MLA who voted in favour of the new legislation.
Amnesty International said failing to reform the law would be a "betrayal of women", while the Northern Ireland Human Rights Commission urged political action.
Northern Ireland Assembly members have voted against legalising abortion in cases of fatal foetal abnormality.