The Assembly voted yesterday, by 58 votes to 29, to allow the bill to complete its first key legislative hurdle.
If the legislation becomes law it would be the first of its kind anywhere in Europe. Similar proposals exist in the Republic.
Green Party Northern Ireland leader Clare Bailey is behind the move and claims it will protect staff and women accessing services.
Laws allowing for the provision of abortion services in Northern Ireland took effect last March, after they were drawn up by Westminster.
Following a public consultation, the government decided not to include powers to establish exclusion zones but said it would keep the matter “under review”.
DUP MLA Jonathan Buckley described the bill as “regressive”.
“Neither I nor my party support abuse or harassment,” he said, adding that he was concerned that “anything from a conversation to a leaflet” would be deemed criminal under the legislation.