We present a new analysis of the observed perturbations of the H i disc of the Milky Way to infer the existence of a dark subhalo that tidally interacted with the Milky Way disc. We examine tidal interactions between perturbing dark subhaloes and the gas disc of the Milky Way using high-resolution Smoothed Particle Hydrodynamics simulations. We compare our results to the observed H i map of the Milky Way to find that the Fourier amplitudes of the planar disturbances are best fit by a perturbing dark subhalo with a mass that is one-hundredth of the Milky Way with a pericentric distance of 5 kpc. This best fit to the Fourier modes occurs about a dynamical time after pericentric approach, when the perturber is 90 kpc from the Galactic Centre. Our analysis here represents a new method to indirectly characterize dark subhaloes from the tidal gravitational imprints they leave on the gaseous discs of galaxies. We also elucidate a fundamental property of parabolic orbits. We show that under certain conditions, one can break the degeneracy between the mass of the perturber and the pericentric distance in the evaluation of the tidal force – to directly determine the mass of the dark perturber that produced the observed disturbances.