Snoring and other types of 'sleep disordered breathing', as it is known, can deprive the body of enough oxygen for hours at a time.
Scientists now believe having low blood oxygen levels can trigger the development of cancerous tumours, by promoting the growth of the vessels that feed them.
They say in future doctors could help people fight the disease by stopping them snoring.
Researchers in the US looked at cancer rates in more than 1,500 people, in a study of sleep problems that has been going for 22 years.
They found those with severe sleep disordered breathing (SDB) were 4.8 times more likely to develop cancer than those who had no such problems.
Those with moderate SDB were at double the risk, while those with only a slight problem had a 10 per cent increased chance, according to the group, from the University of Wisconsin-Madison.
By far the most common type of sleep disordered breathing problem is obstructive sleep apnoea.
In this, the airway frequently collapses during the breathing cycle, leaving the sleeper struggling for breath. Typically this produces snoring and repeated forced waking.
Sleep apnoea is already known to be associated with other health problems including obesity, diabetes, high blood pressure, heart attacks and strokes.
As being overweight can cause cancer, it could simply have been the case that snoring had no active role in promoting cancer, and was simply a proxy for obesity.
However, the researchers took into account whether participants were a healthy weight or not, as well as a range of other confounding factors, such as age, sex, and smoking status.
The link between SDB and cancer held true even after these were adjusted for. In fact, the association was stronger for those of a healthy weight than the obese.
The researchers concluded this meant that sleep disordered breathing could itself raise the risk of cancer, rather than just being a general sign of poor health.
Laboratory studies have also shown that intermittent hypoxia - or low oxygen levels - promotes tumour growth in mice with skin cancer. Lack of oxygen stimulates the generation of blood vessels that nourish tumours, a process known as angiogenesis.
Dr Javier Nieto, who led the study, said: "The consistency of the evidence from the animal experiments and this new epidemiologic evidence in humans is highly compelling."
Laboratory and animal studies "suggest that intermittent hypoxia promotes angiogenesis and tumour growth".
He continued: "Ours is the first study to show an association between SDB and an elevated risk of cancer mortality in a population-based sample."
He said further research was needed to prove the link beyond doubt, but said if the relationship was firmy established, "the diagnosis and treatment of SDB in patients with cancer might be indicated to prolong survival".
The results were presented on Sunday at the annual conference of the American Thoracic Society in San Francisco. They will also be published in the American Journal of Respiratory and Critical Care Medicine.