The passenger jet was undergoing maintenance and no one is believed to have been on board at the time, but an employee spotted the man and called airport police, who reportedly arrived in two minutes and apprehended the man.
The student, who is believed to be from Trinidad, parked his red sedan on a road near the runway at around 2am, before jumping over the fence, running across the apron and boarding the American Airline Airbus A321, airport spokeswoman Lori Booker told CNN.
"There obviously seemed to be planning involved," she said.
A sticker on his car indicated he lived in the area at least recently, as did some of his social media posts, she said, adding she was not sure which flight school he attended.
The man is yet to be identified and his motive remains a mystery.
The airport remained on lockdown for five hours, returning to business as usual by 7am and with only two flights affected.
"We are now a fully functioning airport," Ms Booker told reporters. "We believe in this instance our security worked just fine."
Melbourne Police Department, FBI agents and members of the Joint Terrorism Task Force all attended the scene.
Authorities searched the car with a robotic arm before towing it away around 7.30am.
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