We aim to understand under which conditions a low-mass planet can open a gap in viscous dusty protoplanetary discs. For this purpose, we extend the theory of dust radial drift to include the contribution from the tides of an embedded planet and from the gas viscous forces. From this formalism, we derive (I) a grain-size-dependent criterion for dust gap opening in discs, (II) an estimate of the location of the outer edge of the dust gap and (III) an estimate of the minimum Stokes number above which low-mass planets are able to carve gaps that appear only in the dust disc. These analytical estimates are particularly helpful to appraise the minimum mass of a hypothetical planet carving gaps in discs observed at long wavelengths and high resolution. We validate the theory against 3D smoothed particle hydrodynamics simulations of planet-disc interaction in a broad range of dusty protoplanetary discs. We find a remarkable agreement between the theoretical model and the numerical experiments.