The figure is above the first estimate of Aus$5.8 billion for the damage caused by the deadly floods that swamped thousands of homes and paralysed the state capital Brisbane and were followed within days by Cyclone Yasi.
"I expect the cost of our natural disasters to be above that initial forecast, and exceed the Aus$6 billion figure," Fraser told an economic forum.
Australia suffered historic floods in December and January that swamped coal mines, ruined roads and other infrastructure and destroyed crops and farmland in Queensland and are set to impact on national growth.
Fraser said the extraordinary weather events, including Yasi, which wrecked towns and crops in the state's north, were a "kick in the guts for Queensland's economy", which had been enjoying strengthening business conditions in 2010.
The floods and storms had smashed exports from the coal-producing state, which had also suffered from a natural disaster in Queensland's major trading partner Japan following a massive earthquake and tsunami there in March.
"Presently we face enormous and immediate challenges in kicking over the flooded engine of the state's economy," Fraser said.