For the interpretation of measurements of radio emission from extensive air showers, an important systematic uncertainty arises from natural variations of the atmospheric refractive index n. At a given altitude, the refractivity N=106(n−1) can have relative variations on the order of 10% depending on temperature, humidity, and air pressure. Typical corrections to be applied to N are about 4%. Using CoREAS simulations of radio emission from air showers, we have evaluated the effect of varying N on measurements of the depth of shower maximum Xmax. For an observation band of 30–80 MHz, a difference of 4% in refractivity gives rise to a systematic error in the inferred Xmax between 3.5 and 11 g/cm2, for proton showers with zenith angles ranging from 15 to 50°. At higher frequencies, from 120 to 250 MHz, the offset ranges from 10 to 22 g/cm2. These offsets were found to be proportional to the geometric distance to Xmax. We have compared the results to a simple model based on the Cherenkov angle. For the 120−250 MHz band, the model is in qualitative agreement with the simulations. In typical circumstances, we find a slight decrease in Xmax compared to the default refractivity treatment in CoREAS. While this is within commonly treated systematic uncertainties, accounting for it explicitly improves the accuracy of Xmax measurements.