The possibility to grow in zincblende (ZB) and/or wurtzite (WZ) crystal phase widens the potential applications of semiconductor nanowires (NWs). This is particularly true in technologically relevant III–V compounds, such as GaAs, InAs, and InP, for which WZ is not available in bulk form. The WZ band structure of many III–V NWs has been widely studied. Yet, transport (that is, carrier effective mass) and spin (that is, carrier g-factor) properties are almost experimentally unknown. We address these issues in a well-characterized material: WZ indium phosphide. The value and anisotropy of the reduced mass (μ_exc) and g-factor (g_exc) of the band gap exciton are determined by photoluminescence measurements under intense magnetic fields (B, up to 28 T) applied along different crystallographic directions. μ_exc is 14% greater in WZ NWs than in a ZB bulk reference and it is 6% greater in a plane containing the WZ ĉ axis than in a plane orthogonal to ĉ. The Zeeman splitting is markedly anisotropic with g_exc = |g_e| = 1.4 for B⊥ĉ (where g_e is the electron g-factor) and g_exc = |g_e – g_h,//| = 3.5 for B//ĉ (where g_h,// is the hole g-factor). A noticeable B-induced circular dichroism of the emitted photons is found only for B//ĉ, as expected in WZ-phase materials.