We present a framework to determine nonequilibrium steady states in strongly correlated electron systems in the presence of dissipation. This is demonstrated for a correlated electron (Falicov-Kimball) model attached to a heat bath and irradiated by an intense pump light, for which an exact solution is obtained with the Floquet method combined with the nonequilibrium dynamical mean-field theory. On top of a Drude-like peak indicative of photometallization as observed in recent pump-probe experiments, new nonequilibrium phenomena are predicted to emerge, where the optical conductivity exhibits dip and kink structures around the frequency of the pump light, a midgap absorption arising from photoinduced Floquet subbands, and a negative attenuation (gain) due to a population inversion.