Atrial fibrillation raises the risk of stroke and causes heart-related chest pain or heart failure in some people.
Researchers in the Atherosclerosis Risk in Communities Study (ARIC) followed 10,009 middle-aged people for an average 13.6 years.
Atrial fibrillation developed at a rate of 5.7 incidents per 1,000 person-years in those with no retina or kidney changes.
There were 8.9 incidents per 1,000 person-years in those with signs of small vessel damage in the retina, such as micro-bleeds or micro-aneurysms.
There were 16.8 incidents per 1,000 person-years in those with signs of vessel damage in the kidneys, allowing tiny amounts of protein to be released into their urine (micro-albuminuria) and 24.4 incidents per 1,000 person-years in those with both retinopathy and micro-albuminuria.
Though reasons for the association are unclear, changes in other vascular beds may serve as a representation of coronary micro-vascular changes and the observed association may be mediated via inflammation, endothelial dysfunction, autonomic dysfunction, and electro-mechanical remodelling, the researchers said.
The research was presented at the American Heart Association's Scientific Sessions 2013 in Dallas.