Describing the "riotous" progress in the biotechnology industry on Tuesday, the report concluded that the world may soon face horrific dangers should yet more advances continue unchecked.
Biotechnology is already near a stage where devastating diseases can be recreated and illnesses created that could target specific ethnic groups, says the study's author.
Malcolm Dando, head of peace studies at Bradford University in northern England, has studied biological weapon development for 20 years and says genetically-engineered anthrax and synthetic versions of polio could create havoc.
"What we are talking about here is the development of a technology which could clearly be misused," Dando told a London news conference.
"We have a much more difficult problem in controlling biological weapons [as opposed to nuclear] in the long term," he said. "If life sciences are misused, there are major threats to human rights, human dignity and human safety."
In 1999, the BMA called for the strengthening of the 1975 Biological and Toxin Weapons Convention to stop the spread of biological and chemical weapons.
But Monday's report on biological weapons, the second in five years, warned that the window of opportunity to tackle the spread of these biological weapons was shrinking fast.
Dr Vivienne Nathanson, head of science at the BMA, said it was appropriate for a medical body to report on weapons of mass destruction.
"As far as doctors are concerned, the issue of weapons control is important, because at the end of the day doctors literally pick up the pieces," she said.
The reason for publishing a second report only five years after the first was because biological science had developed so rapidly, she said. "It's never been easier to develop biological weapons - all you have to do is look on the internet."
"The situation today is arguably worse than it was when we published our last report five years ago," Nathanson said.