We show that application of a magnetic field induces optical second-harmonic generation (SHG) in GaAs. This phenomenon arises from field-induced symmetry breaking causing new optical nonlinearities. A series of narrow SHG lines is observed in the spectral range from 1.52 to 1.77 eV that we attribute to Landau-level quantization of the band energy spectrum. The rotational anisotropy of the SHG signal distinctly differs from that of the electric-dipole approximation. Model calculations reveal that nonlinear magneto-optical spatial dispersion that comes together with the electric-dipole term is the dominant mechanism for this nonlinearity.