The optical transmission of Bridgman-grown Cd1-xMnxSe (x ≤ 0.45) has been studied at 4.2K in the neighborhood of the absorption edge for magnetic fields H up to 27T. The experiments were carried out in the Voigt configuration for magnetic field orientations parallel and perpendicular to the c-axis. A grating spectrometer combined with a diode detector array was used to make wavelength scans of 40nm at fixed magnetic fields. For all x-values the absorption edge shifted to longer wavenumbers with increasing magnetic field and the shift was approximately proportional to the magnetization. Additional magnetic-field-induced structure near the absorption edge was also observed.