Sports Minister Carál Ní Chuilín says she will not provide £26m funding for the redevelopment of Windsor Park until the IFA has "appropriate governance".
The IFA scrapped the requirement for suitability assessments for senior officials earlier this year.
"I need to be assured that appropriate governance and accountability structures have been maintained," said the minister in the Assembly.
"Until that happens, I can't sign off on any agreement."
The controversy centres on the appointment of Amateur League official David Martin as vice-president of the Irish Football Association.
Members of the IFA's council unanimously backed Martin for the position - even though he had been forced to resign from the same post three years ago and had subsequently failed a suitability test for senior office.
Martin's 2010 resignation was a result of his role in the unfair dismissal of Howard Wells as IFA chief executive, something which cost the association £500,000. The then president Raymond Kennedy also had to stand down.
"Any organisation that is in receipt of funding from government has an appropriate responsibility to ensure governance is upheld," the minister added.
"DCAL (Department of Culture, Arts and Leisure) is working with the IFA to review the implications of recent changes to their articles of association."
In a later statement the minster said: "We expect these matters can be resolved by the IFA expediently and to DCAL's satisfaction, thereby ensuring the redevelopment of Windsor Park remains on schedule."
The IFA responded by saying it welcomes the minister's comments and "looked forward to continuing to work with them (DCAL) to deliver all the benefits that a national stadium promises".
Northern Ireland manager Michael O'Neill said last week that it is vital the redevelopment of Windsor Park goes ahead without any delays.
Meanwhile, NI supporters groups have urged the IFA to ensure that government funding for the stadium is not put in jeopardy.
Martin is a long-serving officer of the Northern Amateur Football League which has 94 IFA-affiliated clubs.
He could be a candidate for the IFA presidency in 2015 when present incumbent Jim Shaw's five-year term is due to end.
The stadium redevelopment work will see two new stands at Windsor Park, plus the refurbishment of two others increasing the capacity from 12,000 to 18,000.
Also planned are new lights, under-pitch heating and drainage, a museum and conference facilities.