We study optical transitions from a periodic array of InP/InAs/InP core-multishell nanowires (CMNs) having a wurtzite crystal structure by using photoluminescence (PL) and PL excitation (PLE) spectroscopy. Observing a large Stokes shift between PL and PLE spectra, a blueshift of the PL peak with a cube-root dependence on the excitation power and a slow and nonexponential decay of PL with an effective decay time of 16 ns suggest a type-II band alignment. Band-offset calculation based on the “model-solid theory” of Van de Walle [Phys. Rev. B 39, 1871 (1989)] supports type-II band lineup if the InAs layer in the wurtzite CMNs is assumed to sustain compressive strain in all directions.