Mechanical force controls fundamental cellular processes in health and disease, and increasing evidence shows that the nucleus both experiences and senses applied forces. Such forces can lead to the nuclear translocation of proteins, but whether force controls nucleocytoplasmic transport, and how, remains unknown. Here we show that nuclear forces differentially control passive and facilitated nucleocytoplasmic transport, setting the rules for the mechanosensitivity of shuttling proteins. We demonstrate that nuclear force increases permeability across nuclear pore complexes, with a dependence on molecular weight that is stronger for passive than for facilitated diffusion. Owing to this differential effect, force leads to the translocation of cargoes into or out of the nucleus within a given range of molecular weight and affinity for nuclear transport receptors. Further, we show that the mechanosensitivity of several transcriptional regulators can be both explained by this mechanism and engineered exogenously by introducing appropriate nuclear localization signals. Our work unveils a mechanism of mechanically induced signalling, probably operating in parallel with others, with potential applicability across signalling pathways.