We report the detection of X-ray emission from the jet-driving symbiotic star MWC 560. We observed MWC 560 with XMM-Newton for 36 ks. We fitted the spectra from the EPIC pn, MOS1 and MOS2 instruments with XSPEC and examined the light curves with the package XRONOS. The spectrum can be fitted with a highly absorbed hard X-ray component from an optically-thin hot plasma, a Gaussian emission line with an energy of 6.1 keV and a less absorbed soft thermal component. The best fit is obtained with a model in which the hot component is produced by optically thin thermal emission from an isobaric cooling flow with a maximum temperature of 61 keV, which might be created inside an optically-thin boundary layer on the surface of the accreting with dwarf. The derived parameters of the hard component detected in MWC 560 are in good agreement with similar objects as CH Cyg, SS7317, RT Cru and T CrB, which all form a new sub-class of symbiotic stars emitting hard X-rays. Our previous numerical simulations of the jet in MWC 560 showed that it should produce detectable soft X-ray emission. We infer a temperature of 0.17 keV for the observed soft component, i.e. less than expected from our models. The total soft X-ray flux (i.e. at < 3 keV) is more than a factor 100 less than predicted for the propagating jet soon after its birth (<0.3 yr), but consistent with the value expected due its decrease with age. The ROSAT upper limit is also consistent with such a decrease. We find aperiodic or quasi-periodic variability on timescales of minutes and hours, but no periodic rapid variability. All results are consistent with an accreting white dwarf powering the X-ray emission and the existence of an optically-thin boundary layer around it.