Aims. Herschel-HIFI spectra of H 2 O 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. Methods. A velocity component with an offset of ∼10 km s −1 detected in spectra of the H 2 O 1 10 -1 01 557 GHz transition towards six low-mass protostars in the "Water in star-forming regions with Herschel" (WISH) programme is also seen in higher-excited H 2 O lines. The emission from this component is quantified and local 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. Results. The velocity component is detected in all six targeted H 2 O transitions (E up ∼ 50-250 K), as well as in CO 16-15 towards one source, Ser SMM1. Inferred excitation conditions imply that the emission arises in dense (n ∼ 5 × 10 6 -10 8 cm −3 ) and hot (T ∼ 750 K) gas. The H 2 O and CO column densities are 10 16 and 10 18 cm −2 , respectively, implying a low H 2 O 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 100 AU. 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, IRAS 4A, 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 T rot ∼ 700 K is identified as arising in the same component and traces the part of the shock where H 2 reforms. Thus, H 2 O reveals new dynamical components, even on small spatial scales in low-mass protostars.