Peter Blair, a specialist in medical statistics with the University of Bristol medical school, says babies should not be sleeping in the boxes unless it is a an emergency or rare occasion.
He warns Scottish ministers, in a memo seen by the Guardian, that the high-sided nature of the boxes mean parents must be directly above them to ensure their child is safe.
“They shouldn’t be advocating infants sleep in these boxes unless there isn’t anything else available,” Mr Blair told the Guardian.
Blair's statement to the Scottish Government also suggests that claims the boxes helped cut cot deaths in Finland are based on “tenuous” and unproven evidence, with a warning that the unlaminated boxes could be potential fire risks.
The expert insisted he was "not saying don’t use the baby box."
But he added: "You’ve got to be careful with the advice of how much you can promote it as a safe sleeping space. I think there’s possibilities there but there’s much room for maneouvre and they’re pushing it too far at the moment.”
He added: "We are in ongoing discussions with Peter Blair about his concerns. The baby box meets British safety standards and was awarded British safety standard accreditation as a crib for domestic use – the first non-commercial box in the world to do so,” she said.
But Tory health spokesman Miles briggs said the concerns should have been made public by ministers.
"There are some extremely serious questions for the SNP Government to answer here," he said.
"Parents have been told time and again by Nicola Sturgeon and her ministers that baby boxes are safe.
“Now we learn that a senior expert has raised questions about the evidence base for that in private, and that there are doubts over whether the boxes have the full safety accreditation.
"Why has is taken only now for these concerns to be raised in public? And why, initially at least, did the Scottish Government fail to take Mr Blair's concerns on board?
"If parents are to have faith in these boxes, then we need to see complete transparency from the SNP. This is not a public relations exercise - it is about child safety."
Labour’s Mary Fee said the revelations are “incredibly serious.”
She added: “The Scottish government need to ensure these boxes are safe as a matter of urgency. Labour supports the baby box, and have in the past suggested items that may be of greater use to new mums,but the safety of newborns has to be absolutely paramount.”