Simon Coveney says he hopes international travel will be able to resume "well before" early August.
He said a clearer timeline will be given later this week, but there'll "undoubtedly" be a change to the rules shortly after early July.
It comes as Ryanair has called for EU arrivals to be allowed into Ireland "unrestricted" by July 1st.
The EU is expected to finalise its 'digital green pass' system in the coming weeks - a system aimed at facilitating a return to travel within the bloc.
Member states will be given six weeks to implement the new rules.
On Newstalk Breakfast, Minister Coveney said the green cert system will be in place by July 1st, and he doesn’t believe it will take the full six weeks to implement it for Ireland.
He said it's “very likely” that Irish people will be able to go on holidays abroad later in the summer, and it would be early August "at the very latest".
He said: “Undoubtedly between the start of July and at some point in August there will be a significant change in terms of international travel.”
The Cabinet is due to meet on Friday, with ministers indicating they'll then be able to give a clearer timeline around the return of international travel.
Minister Coveney said: "It will obviously be influenced by public health advice, and by a Government decision.
"Certainly from my perspective, as soon as we can safely do so we should be opening international travel again."
The green pass will allow people to show whether they've been vaccinated, had a negative PCR test, or had COVID-19 within the last six months.
Minister Coveney said it's "unlikely" to be unrestricted travel for all three categories of people.
He said: “If you’ve had COVID and recovered in the last six months, I think it’s quite possible you’ll be asked to take a PCR test before you travel… but you may not have to go into 12 days quarantine. These are the kinds of the decisions we’ll make with the public health teams.
“I think people who are fully vaccinated are of course the ones who will be able to travel without restriction.
“When we have the green cert system up and running I think there’s a very good chance we won’t be applying mandatory hotel quarantine to inter-EU travel."
However, he said the Government will respond if there are any countries in the bloc facing "significant problems" with any new variant.
Ryanair
Meanwhile, Ryanair CEO Michael O'Leary says the tourism industry is "bitterly unhappy" with the current approach to international travels.
The airline wants to see an end to "bizarre and completely useless" mandatory hotel quarantine for arrivals from EU member states.
Mr O'Leary said: "What we’ve been promised on Friday is not a reopening, but an announcement of when eventually they might get around to doing something.
“People are now ignoring the Government restrictions… nobody is booking in May, but from mid-June onwards, as the school holidays take place, we see hundreds of thousands of Irish people heading for the beaches of Portugal, Spain, Italy."
He suggested UK arrivals should be allowed in from June 1st, as they're “way ahead of us” in vaccination and people can already freely cross the border with Northern Ireland.
The Ryanair CEO believes arrivals from the rest of the EU should be allowed in “unrestricted” by July 1st.
He described Eamon Ryan as “without doubt one of the worst transport ministers we’ve ever had in our history”.
He said: “He falls asleep in the Dáil, and in our view, he has been asleep in his office.
“He’s a nice man, he means well… but he’s utterly ineffective.”
