Context. The first unidentified very high energy gamma ray source (TeV J2032+4130) in the Cygnus region has been the subject of intensive search for a counterpart source at other wavelengths. In particular, observations in radio and X-rays are important to trace a population of non-thermal electrons. Aims. A deep (≈ 50 ksec) exposure of TeV J2032+4130 with XMM-Newton has been obtained. The large collection area and the field of view of the X-ray telescopes on-board of XMM-Newton allow to search for faint extended X-ray emission possibly linked to TeV J2032+4130. Methods. The contribution of point sources to the observed X-ray emission from TeV J2032+4130 is subtracted from the data. The point-source subtracted X-ray data are analyzed using blank sky exposures and regions adjacent to the position of TeV J2032+4130 in the field of view covered by the XMM-Newton telescopes to search for diffuse X-ray emission. Results. An extended X-ray emission region with a full width half maximum (FWHM) size of ≈ 12 arc min is found. The centroid of the emission is co-located with the position of TeV J2032+4130. The angular extension of the X-ray emission region is slightly smaller than the angular size of TeV J2032+4130 (FWHM=14± 3 arc min). The energy spectrum of the emission coinciding with the position and extension of TeV J2032+4130 can be modeled by a power-law model with a photon index Γ = 1.5±0.2stat ±0.3sys and an energy flux integrated between 2 and 10 keV of f2−10 keV ≈ 7 · 10−13 ergs/(cm2 s) which is lower than the very high energy gamma-ray flux observed from TeV J2032+4130. The energy flux detected from the extended emission region is about a factor of two smaller than the summed contribution of the point sources present. The energy spectrum can also be fit with a thermal emission model from an ionized plasma with a temperature kBT ≈ 10 keV. Conclusions. We conclude that the faint extended X-ray emission discovered in this observation is the X-ray counterpart of TeV J2032+4130. Formally, it can not be excluded that the extended emission is due to an unrelated population of faint, hot (kBT ≈ 10 keV) unresolved point-sources which by chance coincides with the position and extension of TeV J2032+4130. We discuss our findings in the frame of both hadronic and leptonic gamma-ray production scenarios.