We report efficient electrical injection of spin-polarized carriers from a non-lattice-matched magnetic contact into a semiconductor heterostructure. The semimagnetic semiconductor ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Se}$ is used as a spin-injecting contact on a GaAs-based light-emitting diode. Spin-polarized electrons are electrically injected across the II-VI/III-V interface, where they radiatively recombine in a GaAs quantum well and emit circularly polarized light. An analysis of the optical polarization which includes quantum confinement effects yields a lower bound of 50% for the spin injection efficiency.