Chief executive Michael O’Leary said both the Scottish and UK Governments would be under pressure to ease restrictions when vaccination rates reached high levels.
However, he predicted passengers would have to continue wearing masks until at least spring next year.
His comments came as Ryanair announced new routes between Edinburgh to Naples this summer and Knock this autumn, which were previously operated by other airlines.
First Minister Nicola Sturgeon has said the ban on non-essential international travel may remain in force in Scotland after May 17 – the earliest date the UK Government has said it might be relaxed in England.
Mr O’Leary said: "Everybody is getting very panicked at the moment over international travel, but it’s only the middle of March.
"There isn’t going to be a lot of international travel over what would normally be the Easter period, or in April.
"As the school holidays start through June into July, that will coincide we believe with very high vaccination rates, not just in the UK, also in Europe.
"Therefore we think people should book summer holidays for June, July and August with reasonable confidence at the moment.
"If something changes in that, or the dates move back, there’s no change-fees applicable, so people will simply postpone their holiday plans.
"The Scottish Government will be under as much pressure as Boris Johnson and the Northern Ireland Executive to demonstrate to their constituents that they have had a very successful vaccine programme and that high vaccination rates must result in the removal of restrictions.
"We think that’s inevitably coming through, we think May and June for June and July.”
The Naples route, previously operated by Jet2, is due to start on June 1 and run three days a week – Tuesdays, Fridays and Saturdays.
Flights to Knock, a previous Flybe route, are scheduled to operate on Wednesdays and Sundays from September 1.
Kate Sherry, Edinburgh Airport's aviation director said: “These new Ryanair routes show confidence in the airport’s ability to recover when conditions allow.
"Knowing when those conditions will be met is clearly key for any recovery.
"Unfortunately, we are still waiting for any clear road map.”
A Scottish Government spokesperson said: “We want travel to get back to normal as soon as it is safely possible, but as the First Minister has set out, we must move very carefully to ensure continued suppression of the virus.
"If we open up too much, too quickly then we risk a resurgence of the virus.
"We are clear that non-essential international travel will not be possible before the May 17 target date the UK Government has set, and our view is it might not be possible for a further period after that.
"Some restrictions and requirements, including testing, are likely to remain in place for some time.
“It is vital we do everything possible to prevent the importation of coronavirus, and clearly we cannot risk Covid-19 variants from international travel undermining the deployment of vaccines.
"The clinical advice is clear that a comprehensive system of managed quarantine is essential.”