The local luminescence properties of individual CdSe nanowires composed of segments of zinc blende and wurtzite crystal structures are investigated by low-temperature scanning tunneling luminescence spectroscopy. Light emission from the wires is achieved by the direct injection of holes and electrons, without the need for coupling to tip-induced plasmons in the underlying metal substrate. The photon energy is found to increase with decreasing wire diameter due to exciton confinement. The bulk bandgap extrapolated from the energy versus diameter dependence is consistent with photon emission from the zinc blende-type CdSe sections.