From "Fasting and Eating for Health" by Joel Fuhrman, M.D.:
Vitamin Supplementation During a Fast
Vitamin deficiency attributed to fasting is exceedingly rare. It normally doesn't occur on fasts less than 45 days in length unless the individual was depleted at the onset of the fast. Taking vitamins during a fast in unnecessary and can create unpleasant symptoms.
Many of the physicians who have fasted patients and reported their findings in the medical literature have given vitamins during the fast. However, there is no evidence that this in any way increases the safety of a fast. During a total fast the gastrointestinal tract is better not disturbed with vitamin supplementation.
Sufficient vitamins, minerals, and macronutrients are released in appropriate proportions from tissue stores during the fast. Other physicians than myself who have fasted thousands of patients do not find vitamins of any value during this period. This is confirmed by the observations of other researchers, who noted that vitamin deficiency due to involuntary fasting was very rare among famished populations during World War II, and reported only problems from vitamin supplementation during fasting.
The body's own vitamin reserve more than meets the body's requirements while on a moderate-length fast. It has been proposed that fasting increases the ability of tissues to absorb and utilize nutrients. From my experience, it is clear that we need not worry about the issue of vitamins in a fast of moderate length. I have found that the results of blood tests for vitamin and mineral levels change little during the fast; tests are expensive and unnecessary.