Virgin Australia says it was forced to do manual check-ins for all domestic and international flights as a result of problems affecting the global Sabre system, which is used by airlines around the world.
"As a result, the check-in process may take longer than usual and there may be some delays to flights," Virgin said in a statement.
"We apologise for any inconvenience, and we are working with Sabre to resolve the issue as soon as possible."
A Virgin spokeswoman said the airline had cancelled 35 flights on its domestic and international network and there were currently delays of up to an hour at airports.
The airline said the temporary outage occurred between 2pm (AEST) and 4pm on Tuesday but the disruptions were expected to continue.
"We're working to get it back to normal as soon as possible," the spokeswoman said.
The airline is promising compensation for affected passengers.
In the US, about 50 Alaska Airlines flights were delayed and a spokeswoman at Los Angeles International Airport said 17 flights there had experienced delays of up to 45 minutes.
Officials say other airlines affected include American, Jet Blue, Frontier, Virgin America and British Airways.
The outage represents the second time in four weeks that Virgin has suffered check-in problems.
Last month, a failure in an Optus router resulted in Friday night flights across Australia being cancelled, and the airline needing to put up stranded passengers for the night.
Sabre was installed earlier this year, and replaced the company's Navitaire system, which had a history of outages. In 2011, the airline suffered an 11-day outage due to a failure of the Navitaire system. After Virgin threatened legal action, the matter was eventually settled out of court.
The airline said back in February that it had seen a five-fold increase in bookings since moving to Sabre.