It is not known how many child vegans there are, but based on the adult figures it could be as many as 110,000 under-16s.
Experts note that vegan diets can be perfectly healthy but they can cause serious health problems if pursued without precautions.
A lack of nutrients such as vitamin B12, calcium, zinc and high-quality protein can lead to "irreversible damage" to children's nervous systems or malnutrition, experts warn.
Professor Mary Fewtrell of University College London was to issue the warning at the meeting of the European Society for Paediatric Gastroenterology, Hepatology and Nutrition in Prague on Thursday.
Professor Fewtrell, the chairman of ESPGHAN's nutrition committee says: "It is difficult to ensure a healthy and balanced vegan diet in young infants. The risks of getting it wrong can include irreversible cognitive damage and, in the extreme, death.
"Our advice is that if parents pursue a vegan diet for their child, they must seek and strictly follow medical and dietary advice."
The greatest hazard, she warns, is of vitamin B12 deficiency which can have devastating effects on the brain, nervous system and blood.
Too little protein can lead to stunted growth while too much fibre, another concern in vegan diets, can cause children to feel full too quickly, stopping them getting enough of other nutrients in their food.
Also speaking at the conference, Professor Myriam Van Winckel was to add: "The more restricted the diet of the child, the greater the risk of deficiency and this is by far highest in vegan children.
"Vegan mothers who breastfeed also need to be aware that their children can develop vitamin B12 deficiency between two and 12 months because of the lack of reserves in their body at birth, even if the mother is not showing any signs of deficiency herself."
The nutritionists said: "Parents can be misled by milk supplements".
Rice milk, almond milk and soy milk have a lower nutritional value than dairy milk and as such should not be called milks, but ''drinks'', the researchers warn.
A lack of calcium can lead to the bone disease rickets in children who consume large amounts of non-supplemented soy drink.
The nutritionists said varied vegetarian diets that allow milk or eggs are "generally safe" - and have health benefits such as lower levels of fat, more antioxidants and less risk of being overweight.
Heather Russell, a dietician at the Vegan Society, said it was recognised that certain nutrients need "special attention" when following a vegan diet, such as B12 and also iodine.
Protein can be found in beans, chickpeas, lentils, soya mince and tofu.
She added: "The British Dietetic Association and the American Academy of Nutrition and Dietetics recognise that well-planned vegan diets can support healthy living in people of all ages."