It had been proposed by the DUP chair of the justice committee, Alastair Ross, on behalf of the committee.
However, a petition of concern was submitted to block it.
It was backed by assembly members from Sinn FÃ©in, the Green Party, Alliance and N121.
The amendment proposed that abortions could only be performed lawfully at properties owned by the NHS, unless the circumstances were urgent.
It was defeated following a cross-community vote in which 39 voted for and 41 against.
It was one of a number of proposed changes made during the consideration stage of the Justice Bill that passed early on Wednesday.
Two years ago, another amendment that would have banned private clinics like Marie Stopes was blocked by a similar petition of concern.
Currently Northern Ireland's Marie Stopes clinic is able to provide women with medical terminations, by means of a pill, during the first nine weeks of their pregnancies.
At present, abortion is only legal in  Northern Ireland if a woman's life is at risk or if there is a risk of permanent or serious damage to her mental or physical health.
The situation differs from the rest of the UK, because the 1967 Abortion Act has never been extended to Northern Ireland.
An amendment to tighten the law in Northern Ireland relating to abortion has been defeated in the Assembly.