Herschel-HIFI spectra of H2O towards low-mass protostars show a distinct velocity component not seen in observations from the ground of CO or other species. The aim is to characterise this component in terms of excitation conditions and physical origin. A velocity component with an offset of ~10 km/s detected in spectra of the H2O 110-101 557 GHz transition towards six low-mass protostars in the 'Water in star-forming regions with Herschel' (WISH) programme is also seen in higher-excited H2O lines. The emission from this component is quantified and excitation conditions are inferred using 1D slab models. Data are compared to observations of hydrides (high-J CO, OH+, CH+, C+, OH) where the same component is uniquely detected. The velocity component is detected in all 6 targeted H2O transitions (Eup~50-250K), and in CO 16-15 towards one source, Ser SMM1. Inferred excitation conditions imply that the emission arises in dense (n~5x10^6-10^8 cm^-3) and hot (T~750K) gas. The H2O and CO column densities are ~10^16 and 10^18 cm^-2, respectively, implying a low H2O abundance of 10^-2 with respect to CO. The high column densities of ions such as OH+ and CH+ (both ~10^13 cm^-2) indicate an origin close to the protostar where the UV field is strong enough that these species are abundant. The estimated radius of the emitting region is 100AU. This component likely arises in dissociative shocks close to the protostar, an interpretation corroborated by a comparison with models of such shocks. Furthermore, one of the sources, IRAS4A, shows temporal variability in the offset component over a period of two years which is expected from shocks in dense media. High-J CO gas detected with Herschel-PACS with Trot~700K is identified as arising in the same component and traces the part of the shock where H2 reforms. Thus, H2O reveals new dynamical components, even on small spatial scales in low-mass protostars.