[en] We report the discovery by the HATSouth network of HATS-7b, a transiting Super-Neptune with a mass of 0.120 ± 0.012 $M_{\mathrm{J}}$, a radius of ${0.563}_{-<!--\; ???\; -->0.034}^{+0.046}$ $R_{\mathrm{J}}$, and an orbital period of 3.1853 days. The host star is a moderately bright ($V=13.340\pm <!--\; ??\; -->0.010$ mag, $K_S=10.976\pm <!--\; ??\; -->0.026$ mag) K dwarf star with a mass of 0.849 ± 0.027 $M_{\odot <!--\; ???\; -->}$, a radius of ${0.815}_{-<!--\; ???\; -->0.035}^{+0.049}$ $R_{\odot <!--\; ???\; -->}$, and a metallicity of $[\mathrm{F}\mathrm{e}/\mathrm{H}]$ $=+0.250\pm <!--\; ??\; -->\mathrm{0.080.}$ The star is photometrically quiet to within the precision of the HATSouth measurements, has low RV jitter, and shows no evidence for chromospheric activity in its spectrum. HATS-7b is the second smallest radius planet discovered by a wide-field ground-based transit survey, and one of only a handful of Neptune-size planets with mass and radius determined to 10% precision. Theoretical modeling of HATS-7b yields a hydrogen–helium fraction of 18 ± 4% (rock-iron core and H₂–He envelope), or 9 ± 4% (ice core and H₂–He envelope), i.e., it has a composition broadly similar to that of Uranus and Neptune, and very different from that of Saturn, which has 75% of its mass in H₂–He. Based on a sample of transiting exoplanets with accurately (<20%) determined parameters, we establish approximate power-law relations for the envelopes of the mass–density distribution of exoplanets. HATS-7b, which, together with the recently discovered HATS-8b, is one of the first two transiting super-Neptunes discovered in the Southern sky, is a prime target for additional follow-up observations with Southern hemisphere facilities to characterize the atmospheres of Super-Neptunes (which we define as objects with mass greater than that of Neptune, and smaller than halfway between that of Neptune and Saturn, i.e., $0.054M_{\mathrm{J}}<<!--\; <\; -->M_{\mathrm{p}}<<!--\; <\; -->0.18M_{\mathrm{J}}$).