Planning Landscape Architecture Community Environment (PLACE) has an office in Belfast city centre.
It was one of a number of groups to have its annual funding withdrawn by the ACNI this year.
ACNI said it had to make "difficult strategic funding decisions" due to decreasing income from the National Lottery.
PLACE has been in existence for 15 years and runs a programme of tours, talks, exhibitions and festivals on architecture and the built environment in Northern Ireland.
It also works with community groups and public bodies to advise on urban planning.
A spokesperson for PLACE said the cut was "shocking and disappointing".
The vast majority of arts organisations here would not exist without some form of public subsidy.
The Arts Council distributes millions of pounds of funding towards the running costs of arts groups every year.
About two-thirds of that funding - more than £8m this year - is from the government through the Department for Communities.
The other third - more than £4m - is from the National Lottery.
In recent years government funding to the arts has been cut, but this year it is National Lottery money which the Arts Council says has declined.
That has led to them having to make difficult decisions as demand for funding always outstrips the money they have available.
Groups like PLACE have suffered as a result.
"We were notified without warning that we have been offered three months of funding in order to 'exit' Arts Council of Northern Ireland support," they said.
"This puts PLACE at immediate risk of closure."
"There is no other organisation delivering the same unique mix of activities that PLACE does."
ACNI said they had provided £12.8m of annual funding to 97 arts organisations, a reduction from 102 in 2018-19.
While funding from the Department for Communities to ACNI was the same as last year, lottery funding had reduced by almost 5%.
The ACNI chair John Edmund said they did not have the resources to meet demand.
"Thirty-four organisations were offered standstill funding, five were offered strategic uplifts, while the remainder received cuts," he said.
"Within the context of reducing public funding, this year in particular from the National Lottery, the board had to make the difficult decision to reduce the number of annually funded organisations."
"It is with regret that we had to refuse annual 2019 funding to five current clients."
Among the organisations who have also confirmed to BBC News NI that they have lost ACNI funding this year are Voluntary Arts Ireland - who received £54,580 in 2018/19 - and Terra Nova Productions, who received £19,890 last year.
ACNI has said they will also be offered three months funding to help them exit from its annual funding stream.