An understanding of non-equilibrium carrier dynamics in silicon (Si) nanowires (NWs) and NW heterostructures is very important due to their many nanophotonic and nanoelectronics applications. Here, we describe the first measurements of ultrafast carrier dynamics and diffusion in single heterostructured Si nanowires, obtained using ultrafast optical microscopy. By isolating individual nanowires, we avoid complications resulting from the broad size and alignment distribution in nanowire ensembles, allowing us to directly probe ultrafast carrier dynamics in these quasi-one-dimensional systems. Spatially-resolved pump-probe spectroscopy demonstrates the influence of surface-mediated mechanisms on carrier dynamics in a single NW, while polarization-resolved femtosecond pump-probe spectroscopy reveals a clear anisotropy in carrier lifetimes measured parallel and perpendicular to the NW axis, due to density-dependent Auger recombination. Furthermore, separating the pump and probe spots along the NW axis enabled us to track space and time dependent carrier diffusion in radial and axial NW heterostructures. These results enable us to reveal the influence of radial and axial interfaces on carrier dynamics and charge transport in these quasi-one-dimensional nanosystems, which can then be used to tailor carrier relaxation in a single nanowire heterostructure for a given application.