Sinn Féin, Labour and Independent Ireland deputies left the Dáil chamber, just as Regional Independent TD Carol Nolan stood up to ask a question of Taoiseach Micheál Martin.
People Before Profit-Solidarity TDs also left the Dáil chamber.
Two Social Democrats deputies remained, as Ms Nolan raised an issue relating to special education places in her Offaly constituency.
It was the first time Regional Independent TDs, who are supporting the Coalition, have been able to ask a question under revised Dáil standing orders.
The Social Democrats said they were aware that other political parties would not remain in the Dáil chamber, but "opted to remain".
A spokesperson said: "We are vehemently opposed to the changes to speaking time that the Government has bulldozed through - and have made that clear for months."
Sinn Féin described the walkout as "orderly and dignified".
The party will discuss later what strategy it is to adopt regarding the new speaking slot given to the Regional Independent Group which allows it to ask questions of the Taoiseach.
A spokesperson said the party "definitely" will not stay in the Dáil chamber this week when the slot is called by the Ceann Comhairle.
Meanwhile, the Labour Party has said it is unlikely to attend the new Dáil questions and answer sessions between the Regional Independent group and the Taoiseach.
"The Labour Party has a very limited interest in bearing witness to Government TDs asking questions to the Taoiseach under the guise of other members questions," Party whip Duncan Smith said.
"We have no fixed view on future attendance, but it's unlikely we'll be present very often."
People Before Profit-Solidarity said it plans to never attend the new Dáil questions and answer sessions between the Regional Independent Group and the Taoiseach.
A party spokesperson said they would "urge the rest of the Opposition to do likewise".
Independent Ireland also said its plan "for now" is not to attend the new Dáil questions and answer sessions between the Regional Independent Group and the Taoiseach.
Party leader Michael Collins said: "We do not want to listen to Government TDs asking the Government questions, as if they were Opposition."
In the question that sparked the exodus, Ms Nolan said special education schools are under "enormous pressure" amid surging demand.
Offaly School of Special Education, Tullamore, had "18 applications for just one space", she said.
It is also down two SNAs, which were promised by the Health Service Executive but have not been hired.
This is due to a cap on SNAs and cumbersome paperwork, she added.
Taoiseach Micheál Martin repeated his earlier remarks that the Government wants all parents to have advance notice of the availability of school places for their children.
A row defined by fiery words and chaos has ended in silence.
As Deputy Nolan got to her feet to become the first Regional Independent TD to ask a question of Taoiseach Micheál Martin, the exodus began.
Sinn Féin, Labour, Independent Ireland and People Before Profit deputies quietly headed for the doors.
As one deputy put it to me this morning: "If the Government wants to talk to itself, we don't have to hang around."
Two Social Democrat TDs notably chose to remain in the chamber, as Deputy Nolan raised the issue of special education places in her Offaly constituency.
Eight minutes later, after two questions and two answers, the Dáil resumed its normal business.
A Sinn Féin spokesperson described today's walk out as "orderly and dignified."
Whether that continues when Independent TD Michael Lowry gets a slot to ask questions of Mr Martin is very much an open question.
What's absolutely clear is that the bad blood generated by this lengthy and bitter row continues to course through Leinster House.
TDs from the Regional Independents Technical Group, which also include Michael Lowry, Danny Healy-Rae, Barry Heneghan, Gillian Toole and Mattie McGrath - are now considered not Government or Opposition.
They, along with other Government backbenchers, are being allocated speaking time on Tuesdays and Wednesdays, and get to put questions to the Taoiseach with extra time also provided for them in Minister’s Questions and Private Members' time.
Today's eight-minute midday exchange between the Regional Independent Group representative and the Taoiseach was due to be watched closely, not just for what was said, but also the Opposition reaction.
It comes after Tipperary North TD Mr Lowry said last night's Dáil vote of confidence in Ceann Comhairle Verona Murphy was a significant victory for democracy.
The Dáil voted confidence in the Ceann Comhairle by a substantial majority - 96 votes to 71.
It effectively signalled the end of the Dáil speaking rights row, even if relations between the Government and Opposition are rock bottom.
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Mr Lowry maintained that the position of the Ceann Comhairle was strengthened by last night's Dáil vote.
He described the actions of Opposition parties in recent weeks as juvenile and despicable.
However, the Dáil was told last night by Opposition TDs that the Coalition has entered into what is termed a "grubby deal" with Mr Lowry, and allowing his group ask questions of the Taoiseach is nothing short of a farce.
