Scientists have moved to reassure the public after "rogue" prions that may cause CJD were found in muscle samples taken from patients.
Surgical instruments run a theoretical risk of contamination
Doctors know that, in theory, people may catch CJD if they have an operation using instruments from brain or tonsil surgery on an existing CJD patient.
The latest results, from a Swiss team, raise the remote possibility of transmission after other operations.
However, experts say that this risk, if it exists, would be tiny in comparison.
There are approximately 50 new cases each year of so-called "sporadic CJD" in the UK.
This form of the degenerative disease happens in countries across the world.
These cases are not linked to consumption of BSE-contaminated meat, like the vCJD cases that arose in the 1990s, often in much younger patients.
Instead, they are thought to arise spontaneously in older patients, leading to a very swift decline and death.
The research, published in the New England Journal of Medicine, was carried out by researchers from the University Hospital of Zurich.
They used a very sensitive test to check muscle tissue for signs of abnormal "prions" - malformed body proteins thought to be responsible for the symptoms of all forms of CJD.
They found traces of abnormal prion protein in muscles from eight of 32 patients.
The research did not prove that this very low level of abnormal prion contamination could in practice prove a threat to someone exposed to it.
However, Dr Adriano Aguzzi, who led the research, suggested that it did present at least a theoretical risk.
The Swiss researchers wrote: "Our findings arouse concern about the possibility of iatrogenic (caused by medical treatment) transmission of sporadic CJD."
Studies have suggested that even normally-sterilised surgical instruments could harbour the abnormal prion protein, perhaps passing them on to infect the next patient who goes "under the knife".
There have been five documented cases world-wide of patents developing CJD following surgery with contaminated instruments.
In response, the UK government has already stepped up procedures following "high risk" operations involving parts of the body known to contain larger concentrations of abnormal prions in infected people, such as tonsils and the brain or appendix.
However, a British expert said that even if muscle tissue did pose a risk, it was likely to be tiny in comparison with already-known "high risk" tissues.
Professor Hugh Pennington, president of the Society for General Microbiology, said that it was likely that, given the extra sensitivity of the test used, levels of abnormal prion protein in muscle was hundreds or even thousands time less than in the tonsils or brain of someone carrying the illness.
He told BBC News Online: "Assuming that the findings of this study can be replicated, they are not entirely unexpected.
"It raises the question whether muscle tissue does represent a risk, but even if it does, that risk would be miniscule.
"Procedures on washing and sterilising surgical instruments have been improved immensely over the past few years.
"There is no evidence that muscle tissue from infected animals is capable of infecting another animal."