We have investigated the optical properties of a single InAsP quantum dot embedded in a standing InP nanowire. Elongation of the transverse exciton-spin relaxation time of the exciton state with decreasing excitation power was observed by first-order photon correlation measurements. This behavior is well explained by the motional narrowing mechanism induced by Gaussian fluctuations of environmental charges in the nanowire. The longitudinal exciton-spin relaxation time is evaluated by the degree of the random polarization of emission originating from exciton states confined in a single-nanowire quantum dot by using Mueller calculus based on Stokes parameters representation. The reduction in the random polarization component with decreasing excitation power is caused by suppression of the exchange interaction of electron and hole due to an optically induced internal electric field by the dipoles at the wurtzite and zinc-blende heterointerfaces in the InP nanowire. © 2012 American Physical Society.