We probe the electron transport properties in the shell of GaAs/In0.2Ga0.8As core/shell nanowires at high electric fields using optical pump / THz probe spectroscopy with broadband THz pulses and peak electric fields up to 0.6 MV/cm. The plasmon resonance of the photoexcited charge carriers exhibits a systematic redshift and a suppression of its spectral weight for THz driving fields exceeding 0.4 MV/cm. This behavior is attributed to the intervalley electron scattering resulting in the increase of the average electron effective mass and the corresponding decrease of the electron mobility by about 2 times at the highest fields. We demonstrate that the increase of the effective mass is non-uniform along the nanowires and takes place mainly in their middle part, leading to a spatially inhomogeneous carrier response. Our results quantify the nonlinear transport regime in GaAs-based nanowires and show their high potential for development of nano-devices operating at THz frequencies.