The Minister said Ireland already has "an aggressive suppression strategy".
A Zero Covid strategy being implemented would mean not opening schools and restrictions lasting until at least September or even November, according to Health Minister Stephen Donnelly.
The Minister also said it would "probably" require returning to 2km restrictions as opposed to the current 5km limit.
He made the comments during a debate in the Seanad where the Labour Party called for mandatory hotel quarantine for all non-essential international arrivals, as opposed to just those arriving from high risk countries.
Labour Senator Ivana Bacik said she wanted "a national aggressive suppression strategy" and a Zero Covid approach similar to New Zealand.
However, Donnelly said: "For what it is worth, Zero Covid is a very seductive idea. We can look at New Zealand and ask 'can we not just have that?'.
"The answer that I have got from the Chief Medical Officer, from NPHET and from various experts is that it does not work in Ireland.
"New Zealand is an island 3,500 km into the Pacific Ocean that was not dealing with a more contagious variant, that got down to a very low level and was able to successfully implement it."
Donnelly said he believes Ireland already has an aggressive suppression strategy in place and that the main difference between the Government's current approach and a Zero Covid approach was "time".
About the latter, he said: "It would require keeping the Level 5 measures in place now for months and months. I do not know how long, but September, October or November.
"It would require not opening the schools. It would probably require going back to a 2km measure for our homes."
Meanwhile, the Seanad passed the bill to introduce mandatory hotel quarantine measures.
They will apply to the 33 countries where the risk of Covid-19 transmission or mutations of the disease are high.
