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 textit{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 black body plus a power law, with $k_{rm B}T = 0.07^{+0.04}_{-0.03}$~keV and a photon index $Gamma= 1.0pm0.8$, respectively. The non-thermal component dominates above $simeq$0.8 keV. The obtained total flux is $F(0.3$--$5.5~{rm keV}) = (4.6^{+1.3}_{-1.1})times10^{-14}$ erg cm$^{-2}$ s$^{-1}$. At a distance of $2.6pm0.6$~kpc the total flux translates into a luminosity $L_{rm X} = (3.7pm1.7)times10^{31}$ erg s$^{-1}$. Considering the estimated range of BH masses to be 3.8--6.9 $M_{odot}$, this luminosity represents $(6.7pm4.4)times10^{-8}~L_{rm Edd}$, 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 $sim10^{-8} L_{rm Edd}$. MWC~656 will allow the accretion processes and the accretion/ejection coupling at very low luminosities for BH~HMXBs to be studied.
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