According to a spokesperson for the airport, terminal four has been closed since 9:00 p.m. local time (10:00 a.m. GMT).
"We are responding and working with the relevant authorities over a security alert that was directed at Tigerair [Australian airline based in Melbourne Airport]," the spokesperson said, as quoted by ABC News.
The media outlet also cited the Victoria police, saying that the officers have been conducting a search in the airport.
In late December, the Prime Minister of Australia Tony Abbott stated that the terror threat in the country remained high, stressing that "at this level an attack is likely," following a hostage situation in a Sydney cafe.
In December, 17 people were taken hostage in Sydney's Lindt Cafe by a gunman who was later identified by the local police as Man Haron Monis, a self-proclaimed Iranian sheikh. The police stormed the building after a 16-hour siege. Three, including the attacker, were killed in the incident.