Vitamin B12 deficiency can also cause anaemia and inflammation of the nervous system.
Yeast extracts are one of the few vegetarian foods which provide good levels of the vitamin, reports Courier Mail.
The finding was made by Oxford University scientists who used memory tests, physical checks and brain scans to examine 107 people between the ages of 61 and 87.
When the volunteers were retested five years later the medics found those with the lowest levels of vitamin B12 were also the most likely to have brain shrinkage.
It confirms earlier research showing a link between brain atrophy and low levels of B12.
Also, in a new study it was found that drinking too much alcohol can lead to brain shrinkage.
Brain scans of more than 1,800 people found that people who downed 14 drinks or more a week had 1.6 per cent more brain shrinkage than teetotallers.
Women in their seventies were the most at risk.