Ms Noone, a member of the industrial and commercial panel, made the allegations at a private meeting of party TDs and senators in Leinster House on Wednesday night.
The party confirmed that its general secretary, Tom Curran, has been informed of the allegations by chairman Martin Heydon.
“Parliamentary Party Chairman Martin Heydon has written to General Secretary Tom Curran regarding an internal matter within the party,” said a statement.
A party spokesman said: “Due process will be followed and the matter will be dealt with swiftly.
“Fine Gael expects party colleagues to treat all with the utmost respect, professionalism and dignity at all times. Any internal party matters are dealt with the strictest of confidence and Fine Gael will not be making any further comment.”
At the meeting on Wednesday, Taoiseach Leo Varadkar committed to fully investigating the claims, saying that sexism had no place in the party. He said he was disappointed to hear such claims and insisted bullying would not be tolerated within the party.
Justice Minister Charlie Flanagan also stressed that avenues were available within the party to members with concerns of this nature.
Ms Noone’s intervention at the meeting followed a presentation about the party’s efforts to encourage more women to contest elections for Fine Gael.
The Irish Examiner understands that the allegations date back over a number of years, but Ms Noone claims the alleged bullying has intensified since the debate around the referendum on the Eighth Amendment got under way.
It is understood that Ms Noone, who chaired the all-party Oireachtas committee that examined the Eighth Amendment last year, told colleagues that the alleged bullying had become “too much to take” and had got to the point that she “can’t take it anymore”.
“I just want it stopped,” she told colleagues.
A number of members present said Ms Noone was visibly upset while raising the concerns.
She did not name the individual who she said was responsible for the alleged abuse.
Contacted by the Irish Examiner, Ms Noone said she would not be making any comment.
The party figure at the centre of the allegations too had no comment to make, saying there had been no contact from Mr Heydon or Mr Curran.
Ms Noone’s allegations are the second incident to rock the party in recent months.
In November, Barry Walsh resigned from the executive council of Fine Gael over regrets the tone and language he used in tweets that he has posted. He also accepted that some tweets had caused “serious offence” to many people and I apologise unreservedly for that”.
Mr Walsh came under considerable pressure to stand down after it was disclosed that he had posted abusive and personalised tweets.
The issue was brought to light by Dublin Bay South TD Kate O’Connell, who had also sat on the Oireachtas committee on the Eighth Amendment, at a Fine Gael meeting where she presented a series of tweets by Mr Walsh, some of which were directed at her.