Wurtzite InAs nanowire samples grown by chemical beam epitaxy have been analyzed by photoluminescence spectroscopy. The nanowires exhibit two main optical emission bands at low temperatures. They are attributed to the recombination of carriers in quantum well structures, formed by zincblende–wurtzite alternating layers, and to the donor–acceptor pair. The blue-shift observed in the former emission band when the excitation power is increased is in good agreement with the type-II band alignment between the wurtzite and zincblende sections predicted by previous theoretical works. When increasing the temperature and the excitation power successively, an additional band attributed to the band-to-band recombination from wurtzite InAs appears. We estimated a lower bound for the wurtzite band gap energy of approximately 0.46 eV at low temperature.