Laws enabling gardaí to break up house parties could take effect this weekend after it was passed by the Oireachtas.
The legislation now has to be signed in to law by President Michael D Higgins.
However, it will take a number of days before fines for other breaches of Covid-19 rules are operational.
These include not wearing a face covering and traveling further than 5km from home, but are likely to apply to other breaches.
The regulations outlining the exact penalties and what specifically they apply to will be drawn up in the coming days and published later next week.
The Department of Health has said that the new regulations to introduce the fines will be updated as a priority following consultation with the Minister for Justice.
The Dáil passed legislation this afternoon empowering gardaí to levy new fines on people who breach Covid-19 regulations by 85 votes to 53.
In the upper house this evening, several senators flagged concerns that the bill was not workable.
It is understood that former Fine Gael minister Michael Ring did not vote on the legislation. He had told RTÉ's News at One that he would abstain over concerns about the 5km travel limit, especially in rural Ireland.
Earlier, Sinn Féin accused the Government of asking for a blank cheque to impose fines for breaching public health rules without adequate scrutiny.
Sinn Féin's David Cullinane criticised the move to "rush" the legislation through the Dáil and Seanad in one day.
He said some enforcement was needed, but his party has issues with several aspects of the bill and could not support it unless its amendments were accepted.
Mr Cullinane said the minister wanted the opposition to write him a blank cheque to draft regulations, although they did not know exactly what the fines would be and had no opportunity to ensure proper checks and balances are in place.
Labour leader Alan Kelly said the party would support the bill but did so with great and serious reservations.
He said the regulations must be examined in the Dáil before they come in to force.
Mr Kelly said he believed there was widespread but considered support for the regime, but that could collapse if the Government got it wrong.
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Introducing the bill, Minister for Health Stephen Donnelly said tougher enforcement was needed for the small number of people who make a conscious decision not to follow public health rules.
He said their actions put at risk the enormous sacrifices of everyone else.
Mr Donnelly said enforcement would be used as a last resort and the vast majority of people are compliant.
The bill provides for tiered fines starting at €1,000 for various offences.
Further fines for breaching the 5km travel rule would specified in regulations to be drafted by the Ministers for Health and Justice and could be levied at a maximum of €500, but are likely to be less.
Mr Donnelly indicated the fine for not wearing a mask could be €50.
People Before Profit TD Bríd Smith said the party was totally opposed to the fines and they were a panic move to deflect from other problems.
She said there would be a surge of fines against people from the lower economic classes.
"You're not going to find the gardaí walking up the leafy suburbs of Castleknock, stopping somebody in their SUV with a crate of fine pinotage wine going to a dinner party.
"What you'll find is they will stop young lads and young ones going through parks with a six pack under their arm," she said.
Independent TD Verona Murphy asked whether a landlord could face a fine for the behaviour of their tenants and she said that would be outrageous.
She said the fines system had many inconsistencies and a PhD was necessary to understand them.
Additional reporting Mary Regan