MWC 656 (=HD 215227) was recently discovered to be the first binary system composed of a Be star and a black hole (BH). We observed it with XMM-Newton, and detected a faint X-ray source compatible with the position of the optical star, thus proving it to be the first Be/BH X-ray binary. The spectrum analysis requires a model fit with two components, a blackbody plus a power law, with (ProQuest: Formulae and/or non-USASCII text omitted) keV and a photon index Gamma = 1.0 + or - 0.8, respectively. The non-thermal component dominates above Asymptotically = to0.8 keV. The obtained total flux is (ProQuest: Formulae and/or non-USASCII text omitted) erg cm super(-2) s super(-1). At a distance of 2.6 + or - 0.6 kpc the total flux translates into a luminosity L sub(x) = (3.7 + or - 1.7) x 10 super(31) erg s super(-1). Considering the estimated range of BH masses to be 3.8-6.9 M sub(middot in circle), this luminosity represents (6.7 + or - 4.4) x 10 super(-8)L sub( Edd), which is typical of stellar-mass BHs in quiescence. We discuss the origin of the two spectral components: the thermal component is associated with the hot wind of the Be star, whereas the power-law component is associated with emission from the vicinity of the BH. We also find that the position of MWC 656 in the radio versus X-ray luminosity diagram may be consistent with the radio/X-ray correlation observed in BH low-mass X-ray binaries. This suggests that this correlation might also be valid for BH high-mass X-ray binaries (HMXBs) with X-ray luminosities down to ~10 super(-8)L sub(Edd). MWC 656 will allow the accretion processes and the accretion/ejection coupling at very low luminosities for BH HMXBs to be studied.