We present a new approach to studying the initial mass function (IMF) in external galaxies based on quasar microlensing observations. We use measurements of quasar microlensing magnifications in 24 lensed quasars to estimate the average mass of the stellar population in the lens galaxies without any a priori assumption on the shape of the IMF. The estimated mean mass of the stars is < M> ={0.16}-0.08+0.05 {M}☉ (at the 68% confidence level). We use this average mass to put constraints on two important parameters characterizing the IMF of lens galaxies: the low-mass slope, α 2, and the low-mass cutoff, M low. Combining these constraints with prior information based on lensing, stellar dynamics, and absorption spectral feature analysis, we calculate the posterior probability distribution for the parameters M low and α 2. We estimate values for the low-mass-end slope of the IMF < {α }2> =-2.6+/- 0.9 (heavier than that of the Milky Way) and for the low-mass cutoff < {M}low}> =0.13+/- 0.07. These results are in good agreement with previous studies of these parameters and remain stable against the choice of different suitable priors.