Magnetization-induced second-harmonic generation is observed in magnetic photonic-crystal microcavities. The microcavity is formed from a half-wavelength-thick Bi-substituted yttrium-iron-garnet film sandwiched between two high-finesse dielectric Bragg reflectors. The transversal nonlinear magneto-optical Kerr effect reveals itself in magnetization-induced variations of the intensity and the relative phase of the second-harmonic wave. The variations reach the factor of 4 in intensity and 180degrees in phase for opposite directions of the dc-magnetic field. The longitudinal and polar nonlinear magneto-optical Kerr effects manifest themselves in the considerable, up to 50degrees, rotation of the second-harmonic wave polarization.