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 = |ge| = 1.4 for B⊥ĉ (where ge is the electron g-factor) and g exc = |ge - gh,//| = 3.5 for B//ĉ (where gh,// 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.