We present first-principles calculations of the optical properties of zigzag-edged graphene nanoribbons (ZGNRs) employing the GW-Bethe-Salpeter equation approach with the spin interaction included. Optical response of the ZGNRs is found to be dominated by magnetic edge-state-derived excitons with large binding energy. The absorption spectrum is composed of a characteristic series of exciton states, providing a possible signature for identifying the ZGNRs. The edge-state excitons are charge-transfer excitations with the excited electron and hole located on opposite edges; they moreover induce a spin transfer across the ribbon, resulting in a photoreduction of the magnetic ordering. These novel characteristics are potentially useful in the applications.