Australian Transport Minister John Anderson said Flight 840 turned back to Sydney airport 90 minutes after taking off.
However, Anderson told the Australian Broadcasting Corp., he believes the note is a hoax.
When the note was shown to the pilot, the plane turned around and dumped its fuel after the pilot consulted with U.S. company officials.
Air space around the airport was temporarily shut down to allow the plane to land.
Anderson said a search of the aircraft had so far failed to reveal any bombs.
The 246 passengers and 18 crew on board the flight were taken away by bus and were rescheduled to fly Wednesday.