According to the IQ Comparison Site, the average IQ of medical doctors is around 120 points. This data is taken from a 2002 study that tested the IQs of people in several dozen different professional fields. Doctors had the highest average of the fields tested in the study.
The IQ spread for the doctors tested in the study ranged from 105 to 132 points. According to the most commonly used scale for interpreting IQ scores, this means that the majority of doctors have average or above-average intelligence, with a few even heading into the "moderately gifted" range of the spectrum.