If this is above a certain thickness it can restrict the blood flow to the brain and increase the risk of a stroke.
Reduces the risk of stroke
The study is the first of its kind to examine how eating certain vegetables can affect the blood vessels.
Researchers from the University of Western Australia in Crawley distributed food questionnaires to 954 women aged 70 and over.
They then performed ultrasound tests to measure the thickness of their carotid arteries.
The carotid arteries for women who ate three or more portions of vegetables a day were 0.05mm thinner than those who ate none.
Although this is only a fractional difference, reducing the thickness by just 0.1 mm can lower the risk of stroke by up to a fifth.
The study, published in the Journal of the American Heart Association, also found that cruciferous vegetables were particularly effective.
Vegetables tackle underlying cause of heart disease
The carotid arteries thicken due to the build-up of plaque, formed by fatty deposits.
If these are thick it is likely that other blood vessels around the body are also thick, a condition known as atherosclerosis.
This greatly increases the risk of heart attacks and strokes.
Dr Lauren Blekkenhorst, the lead author said: "This is one of only a few studies that have explored the potential impact of different types of vegetables on measures of subclinical atherosclerosis, the underlying cause of cardiovascular disease.
"After adjusting for lifestyle, cardiovascular disease risk factors (including medication use) as well as other vegetable types and dietary factors, our results continued to show a protective association between cruciferous vegetables and carotid artery wall thickness.
"Still, dietary guidelines should highlight the importance of increasing consumption of cruciferous vegetables for protection from vascular disease."
Although the study was carried out in women, similar benefits are likely to be seen in men.