Members of the Oireachtas Golf Society, including TDs and Senators, were set to be interviewed by gardaí as part of the investigation into a dinner held at a hotel in Co Galway on Wednesday night.
Informed sources said that while it was not a criminal offence to attend such an event, any of those who organised it would be investigated and could be criminally prosecuted.
Anyone convicted of organising an event in breach of the Covid-19 regulations faces fines of up to €2,500 and/or up to six months in prison.
A number of people have already been convicted and jailed for short periods for more minor Covid-19-related offences, including being more than 2km or 5km from home without a legitimate excuse during the strict lockdown period.
Invitations for the golfing event were issued by society captain Noel Grealish TD (Independent) and society president Donie Cassidy, a former Fianna Fáil senator.
Tánaiste and Fine Gael leader Leo Varadkar said on Friday morning the event was "organised by the Oireachtas Golf Society" and that it "should not have happened".
Fianna Fáil's Dara Calleary has resigned from his position as minister for agriculture over his attendance while Fine Gael's Jerry Buttimer has resigned as leas-cathaoirleach of the Seanad.
Among those in attendance were Ireland's EU commissioner Phil Hogan and Supreme Court judge and former attorney general Mr Justice Séamus Wolfe.
A total of 81 people attended the dinner in Clifden, Co Galway, which was far in excess of the limits permitted for indoor gatherings under the Covid-19 regulations.
On Tuesday, some 24 hours before the golfing event, the number of people permitted at indoor events was lowered by the Government to a maximum of six, down from 50.
Garda Headquarters confirmed on Friday that it was investigating a possible breach of the regulations introduced to combat Covid-19 introduced under the Health Act.
"As this is an active investigation An Garda Síochána has no further comment," the Garda said in a brief statement.
The Irish Times understands gardaí would now seek to establish who within the Oireachtas Golf Society organised the event and whether they had any outside assistance, perhaps from hotel staff.
Under a section in the Covid-19 regulations relating to “restrictions on events” it states “a person shall not organise, or cause to be organised” an event. While measures relating to social distancing are advisory, and so not enforceable under law, the prohibition on medium and large indoor events is a penal provision, meaning it is a criminal offence.
Garda sources said when the criminal investigating into the Oireachtas golf outing was completed a file would be sent to the Director of Public Prosecutions for a decision on whether criminal charges should be pursued.
A Black Lives Matter protest in Dublin during the lockdown was investigated in the same way.