We calculate the mobility of carriers in a quantum well structure when they are scattered by ionized impurities in the size‐quantum limit (SQL) where the carriers are assumed to populate only the lowest quantized energy level. It is found that the probability of scattering due to ionized impurities decreases with the well thickness in contrast to the case of acoustic phonon scattering where the scattering probability is enhanced under the conditions of the SQL. The temperature and thickness dependence of the mobility depends critically on the screening of the Coulomb potential due to the presence of the ionized impurities.