The magnetization induced in a superconductor due to the reverse proximity effect is studied in hybrid structures containing a superconductor and a ferromagnetic insulator. The study was carried out within the method of semiclassical Green’s functions, in which the Usadel equations are solved numerically with boundary conditions suitable for strongly spin-polarized ferromagnetic materials. The conversion of singlet superconducting correlations into triplet ones as a result of the proximity effect with a ferromagnet and its manifestation in the features of the electron density of states, induced magnetization, and suppression of the superconducting order parameter have been studied. It is shown that the magnetization can change sign inside the superconducting layer. The magnetization distribution is compared with the data obtained by the authors in previous works.