We report X-ray observations of the most distant known gravitationally lensed quasar, J0439+1634 at z = 6.52, which is also a broad absorption line (BAL) quasar, using the XMM-Newton Observatory. With a 130 ks exposure, the quasar is significantly detected as a point source at the optical position with a total of 358 +19 −19 net counts using the EPIC instrument. By fitting a power-law plus Galactic absorption model to the observed spectra, we obtain a spectral slope of Γ = 1.45 +0.10 −0.09 . The derived optical-to-X-ray spectral slope α ox is −2.07 +0.01 −0.01 , suggesting that the X-ray emission of J0439+1634 is weaker by a factor of 18 than the expectation based on its 2500 Å luminosity and the average α ox vs. luminosity relationship. This is the first time that an X-ray weak BAL quasar at z > 6 has been observed spectroscopically. Its X-ray weakness is consistent with the properties of BAL quasars at lower redshift. By fitting a model including an intrinsic absorption component, we obtain intrinsic column densities of N H = 2.8 +0.7 −0.6 × 10 23 cm −2 and N H = 4.3 +1.8 −1.5 × 10 23 cm −2 , assuming a fixed Γ of 1.9 and a free Γ, respectively. The intrinsic rest-frame 2-10 keV luminosity is derived as (9.4−15.1)×10 43 erg s −1 , after correcting for lensing magnification (µ = 51.3). The absorbed power-law model fitting indicates that J0439+1634 is the highest redshift obscured quasar with a direct measurement of the absorbing column density. The intrinsic high column density absorption can reduce the X-ray luminosity by a factor of 3 − 7, which also indicates that this quasar could be a candidate of intrinsically X-ray weak quasar.