Aims: 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. Methods: 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. Results: 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 of 1.6 ± 0.1 g cm-3. Conclusions: 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 {M}_⊕, and the mass of its hydrogen-helium envelope to be 7-23 {M}_⊕. At 0.063 AU, the thermal loss of hydrogen of CoRoT-8b should be no more than 0.1% over an assumed integrated lifetime of 3 Ga. Observations made with SOPHIE spectrograph at Observatoire de Haute Provence, France (PNP.07B.MOUT), and the HARPS spectrograph at ESO La Silla Observatory (081.C-0388 and 083.C-0186). The CoRoT space mission, launched on December 27, 2006, has been developed and is operated by the CNES with the contribution of Austria, Belgium, Brasil, ESA, Germany, and Spain.Both data sets are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/520/A66