The Ceann Comhairle is calling for the Oireachtas Golf Society to be wound up "as a matter of urgency".
It comes amid the controversy over the society's function in Co Galway this week, which 80 people - including Oireachtas members, a minister and a European Commissioner - attended.
Agriculture Minister Dara Calleary has resigned over the controversy, while three Fianna Fáil senators and three Fine Gael senators have lost their party whip for attending the function.
In a statement this evening, Ceann Comhairle Seán Ó Fearghaíl said he has written to the society's secretary following the revelations.
He said: "While recognising that the Golf Society operates independently of the Oireachtas I write to suggest that, in the aftermath of this week's events in Clifden, the society as it is currently structured and named be wound up as a matter of urgency.
"This I believe is a necessary action for the society in the aftermath of this week's events.
"The event has seriously undermined and damaged public confidence in the Oireachtas and in what I hope is our mutual commitment to public health and to the people we serve."
Taoiseach Micheál Martin told RTÉ this evening that the event was a "monumental error of judgement on behalf of all those who attended".
He said he is "deeply, deeply disappointed" with what happened, saying it potentially undermines the public health message about COVID-19.