In a statement, the Australian Border Force said at 11.40am AEST: "Our staff are working hard to minimise earlier delays caused by an outage.
"All issues have now been rectified. We appreciate the patience of passengers at this time and apologise for any inconvenience this may have caused."
Reports said that there were huge delays at Sydney, Melbourne and Perth airports. Brisbane was also affected, but Adelaide escaped.
Neither Melbourne nor Sydney airports have any information on their Twitter feeds as they did in April.
Over the last few days, a number of flights have been delayed by strong winds.