The budget airline’s website states that people who do not check-in online will be charged £55 per passenger to do so at the airport counter.
In a statement, the company confirmed that the outage caused disruption to airport check-ins and boarding.
"This morning [14 September], we suffered a system outage which caused some short delays at airport check-in and boarding,” a spokesperson for the airline said.
"The system has been restored and flights are operating as normal. We apologise for any inconvenience caused."
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On Twitter, travellers complained to Ryanair about the confusion caused by the outage and said they could not find their flight bookings on the budget airline's mobile app or website.
“Ryanair once again you have surpassed yourselves!” Diana Bond-Smith said. “Chaos at Stansted as the whole Ryanair system is down.”
Graeme Jolly said there was “confusion, chaos and absolute carnage” at the check-in desks at Rome Ciampino.
Meanwhile, Grace O’Driscoll, who said she was due to fly from Nice to Stansted, asked Ryanair to “help urgently", adding: "This is shambolic.”
A spokesperson for Stansted airport said there was a “short disruption” to some of Ryanair’s systems.
No other airlines reported problems this morning, according to the airport.
Agencies contributed to this report