It sure can. One way that fasting effects the periods is by reducing thyroid function. As part of a work-up for irregular periods, I will often look at thyroid function as a cause. Hypothyroidism is common to irregular periods. When a person fasts, the thyroid goes into conserve mode. It slows down metabolism as to not "eat you up" alive. During a fast, the thyroid- believes there is a famine- will lower.