"Nothing was found, there was no actual threat to anybody, just a note, so there was nothing in it," a police spokeswoman who declined to give her name told Reuters.
Police said the 68-passenger turboprop plane with 42 passengers on board on a domestic flight was evacuated at the airport in Albury, in southern New South Wales, and a man was arrested.
Australian Associated Press quoted a passenger as saying he heard someone shout: "Leave your luggage. Get out and run, run, run." It said passengers jumped on to the tarmac.
"Police and emergency services attended Albury airport after receiving information a note was located in the toilet area," a New South Wales state police spokeswoman Emily Waters told Reuters.
She did not say what was written on the note.
Virgin Australia said police met the plane on its arrival "due to a security incident on board". It could not immediately confirm how many passengers were on board.
Australian Prime Minister Malcolm Turnbull said police were treating a deadly siege on Monday in the southern city of Melbourne as an "act of terrorism" after a claim by the Islamic State group that one of its fighters was the gunman responsible.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.