"Safety is our number one priority, but we know this disruption is causing some inconvenience for our passengers and we apologise for that. We are investigating how this incident occurred."
A Twitter user shared that their fully loaded plane was forced to evacuate the terminal and be sent back through security screening.
"They've informed us that someone has slipped through the security gates and entered the terminal without screening," Tim Joyce wrote just before 6.30am on Tuesday.
Mr Joyce spoke to the Today Show from the airport, further explaining his flight was just about to take off when the pilot informed them of the security breach.
"It seems quite serious. There are thousands of people waiting," he said.
"They've pretty much roped everything off. Everything is shut down and everyone has to be rescreened," he said.
"Essentially they've communicated that people will be screened on a boarding basis from now on, so the next flight out will be screened first."
Another passenger from the same Qantas flight to Brisbane shared a similar message on Twitter.
"Everyone had to de plane and are waiting to be called through security again," Sue Duke wrote.
Several flights to about seven different destinations were delayed for more than hour, while others have been cancelled.
The major delays at Melbourne Airport are expected to have flow on effects at other airports across the country.
