Dr Carman said such a change could lead to a cell build-up resulting in a liver disease that often killed children by the age of 5 and showed symptoms in adults later in life.
There was also a risk to animals that ate the wheat throughout the production chain, she said.
Their opinions have been reviewed and endorsed by King's College geneticist Dr Michael Antoniou, who has previously spoken out against GM, but have not been published in a peer-reviewed journal.
Pressure group the Safe Food Foundation responded by calling on CSIRO to immediately release all details of its safety testing for "urgent independent scientific review", or else cease all field trials.
A CSIRO spokesman said the claims would be considered by the agency.
The chief executive of New Zealand industry body Agcarm, Graeme Peters, dismissed criticisms of the agency as "grubby and intellectually weak politics".
"There are those who seek to exploit the fear of the unknown and there are those who try instead to understand it - field trials of new technology are a technique for understanding the benefits and impacts of new technology," he said.
Australia is on track to become the first country in the world to allow the commercial growing of GM wheat, and major GM players pushed for New Zealand to loosen its strict regulations during an international biotech conference in Rotorua last week.
GE Free NZ president Claire Bleakley claimed GM wheat could produce serious health effects.
She said GM funders had turned seed breeding into "laboratory-patented science which they can manipulate at every turn, starting with soya and corn, and they are now moving to wheat".
The scientists claim
* SiRNA, a form of ribonucleic acid, like DNA, could transfer to humans through food when produced in GM wheat.
* When eaten, the siRNA engineered to suppress the wheat-branching enzyme would also silence the human-branching enzyme which produces energy-storing glycogen.
* This "unbranched" glycogen would have low solubility in human cells and could create build-up in the tissues of the body, especially in the heart and liver.
* This could lead to the disease Glycogen Storage Disease IV, resulting in an enlarged liver, cirrhosis of the liver, and failure to thrive.