A team at the University of Newcastle upon Tyne studied nearly 1,000 women and their newborn babies.
Low birth weight is associated with an increased risk of serious health problems, including respiratory disorders and diabetes.
The research is published in the British Journal of Nutrition.
Women are already advised to take folic acid supplements if trying to conceive, and through the early weeks of pregnancy as the vitamin is known to reduce the risk of neural tube defects such as spina bifida.
But this is the first time the vitamin has been linked to birth weight.