We report the discovery of CoRoT-8b, a dense small Saturn-class exoplanet that orbits a K1 dwarf in 6.2 days, and we derive its orbital parameters, mass, and radius. We analyzed two complementary data sets: the photometric transit curve of CoRoT-8b as measured by CoRoT and the radial velocity curve of CoRoT-8 as measured by the HARPS spectrometer. We find that CoRoT-8b is on a circular orbit with a semi-major axis of 0.063 +/- 0.001 AU. It has a radius of 0.57 +/- 0.02 RJ, a mass of 0.22 +/- 0.03 MJ, and therefore a mean density 1.6 +/- 0.1 g/cm^3. With 67 % of the size of Saturn and 72 % of its mass, CoRoT-8b has a density comparable to that of Neptune (1.76 g/cm^3). We estimate its content in heavy elements to be 47-63 Earth masses, and the mass of its hydrogen-helium envelope to be 7-23 Earth masses. At 0.063 AU, the thermal loss of hydrogen of CoRoT-8b should be no more than about 0.1 % over an assumed integrated lifetime of 3~Ga.