Authorities said they believe the pilot was taking a French tourist on a pleasure flight when the biplane hit the water near the Couran Cove resort on South Stradbroke Island at a high speed, the Australian Broadcasting Corp. reported.
Salvage teams and rescue divers found the wreckage of the plane, but no signs of survivors, police said.
"We've already been conducting a search in the area and the on-scene commander has informed me it's now in the recovery phase," Senior Sgt. Lucas Young said.
ABC said the Australian Transport Safety Bureau will investigate the crash to determine its cause.
The Tiger Moth is a 1930s-vintage biplane used primarily by the air forces of Australia, Britain, Canada and New Zealand as a training aircraft.
Dennis Rodman pledges to end trips to North Korea
Interpol investigating stolen passports on missing flight