I discuss the signatures left by massive neutrinos on the spatial distribution of neutral hydrogen (HI) in the post-reionization era by running hydrodynamic simulations that include massive neutrinos as additional collisionless particles. Our results show that HI is more strongly clustered in cosmologies with massive neutrinos, while its abundance,
ΩHI(z), is lower. These effects arise mainly from the impact of massive neutrinos on cosmology: they suppress both the amplitude of the matter power spectrum on small scales and the abundance of dark matter halos. Modelling the HI distribution with hydrodynamic simulations at z>3, and a simple analytic model at z<3, we use the Fisher matrix formalism to conservatively forecast the constraints that Phase 1 of the Square Kilometre Array (SKA) will place on the sum of neutrino masses.