By serving on the board for even this short period of time, the Donegal businessman is qualified to run for the upcoming Seanad by-election position previously held by Fine Gael MEP Deirdre Clune.
But Fine Gael TDs rounded on Mr Kenny, who personally proposed Mr McNulty and defended his actions.
And Fianna Fail leader Micheal Martin said Mr Kenny had shown "detachment and a sense of arrogance".
Mr Martin accused Taoiseach of showing "a lack of respect for the national institution and has also undermined the Senate once again".
The Irish Independent revealed earlier this week that Mr Kenny overlooked three female party members - Samantha Long, Stephanie Regan, and Councillor Kate O'Connell - in lieu of the relatively unknown Mr McNulty.
Ms Long yesterday resigned from the party, telling this newspaper that the debacle has sent out a "shady image" about Fine Gael's view of women in politics.
"I'm disappointed for Fine Gael women that a regressive step has been taken," she said.
She added: "Geographical consideration came into this."
"It's very unfortunate politics. I have a lot of friends in politics that are noble people and I joined Fine Gael because I thought it was a very noble party,"
Ms Regan, who was also overlooked, told the Irish Independent: "We need to be more mindful that we must work in a manner that gives the public a real confidence in the honesty, integrity and transparancy of what we do and how we do it."
Several Fine Gael TDs said relations have reached a level not seen since before the infamous heave in June 2010.
One backbencher added: "There is a great deal of arrogance creeping in here and we are in a controversy which is quite unnecessary - and it's all of the leadership's own making."
Waterford deputy John Deasy said TDs are becoming "disgusted" at how the party is run.
"The Taoiseach, who likes to give his mobile phone number out to the world, doesn't really engage or entertain criticism," Mr Deasy told RTE radio.
But Mr Kenny said at the Ploughing Championships that appointments to the IMMA board is a prerogative for his Arts Minister, Ms Humphreys.
"I have never given an instruction for a minister to make an appointment," he said.
Meanwhile, both Sinn Fein and Fianna Fail last night demanded that Ms Humphreys answer questions on her role in the fiasco.
A spokesperson for Ms Humphreys confirmed that the IMMA board was increased in size from nine to 11 despite plans to reduce it in the future.
"It is intended to reduce the size of each board to a maximum of nine members. However, this needs to be effected through legislation, which has not yet been published. Publication of this legislation is expected in late 2015."
The spokesperson said that Ms Humphreys became aware of the plans to field Mr McNulty as a Seanad candidate last week.
Speaking yesterday, Ms Humphreys said she had looked at his credentials and decided he was a "good person" for the role before appointing him.
"Sometimes, Dublin-based institutions and important cultural institutions maybe need a greater representation from the regions," she added, referring to the fact that Mr McNulty hails from Donegal. Others within the party said efforts will be made in the coming days to promote Mr McNulty, and to repair the considerable damage already done.
Queries to Mr McNulty through the Fine Gael press office went unanswered.