The already wet ground was unable to recover from the storm, which added another 15-20mm to the week of rain already received.
Umpires had no option but to abandon the game after consulting with ground staff.
The no-result means the teams will receive one point each which will take Queensland up to second spot.
Queensland will take on South Australia from Tuesday in a Marsh Sheffield Shield game that will take place at Ian Healy Oval, the home ground of Northern Suburbs.
The newly revamped Ian Healy Oval will become the 12th venue in Queensland to host first class cricket.
The Ian Healy Oval is the centrepiece of the first two stages of the National Cricket Campus which was officially opened earlier this year.
The $18.6 million campus project is supported by the Australian and Queensland Governments, Brisbane City Council, Cricket Australia, Queensland Cricket and Northern Suburbs District Cricket club.
The Campus comprises three stages across the Shaw Road Redevelopment (Stages A & B) and the Allan Border Field Precinct Redevelopment (Stage C) which will get underway later this year.
The final stages of the project will feature the redevelopment of Allan Border Field starting in June and continuing through until early next year.
The NCC project is jointly funded by the Federal Government, Queensland Government, Brisbane City Council, Cricket Australia, and Queensland Cricket.
The scope of works for the redeveloped Allan Border Field will see the expansion of the oval on the eastern side by 13 metres to bring it into line with ICC requirements for international cricket.
The revamped precinct will see new off-field facilities, improved drainage, terrace seating and the installation of an electric scoreboard.
The upgrade will include five new training wickets as part of the refurbishment of the Ray Lindwall Oval as well as the expansion of the Allan Border Field centre wicket block to include additional pitches.