Context. Pulsars are detected over the whole electromagnetic spectrum, from radio wavelengths up to very high energies, in the GeV-TeV range. While the radio emission site for young pulsars is well constrained to occur at altitudes about several percent of the light-cylinder radius and γ-ray emission is believed to be produced in the striped wind, outside the light cylinder, the non-thermal X-ray production site remains unknown.Aims. The aim of this Letter is to localize the non-thermal X-ray emission region based on a multi-wavelength pulse profile fitting for PSR J2229+6114, which stands as a particularly good candidate given its high X-ray brightness.Methods. Based on the geometry deduced from the joint radio and γ-ray pulse profiles, we fixed the magnetic axis inclination angle and the line-of-sight (LoS) inclination angle. However, we left the region of X-ray emission unlocalized, setting it somewhere between the surface and the light cylinder. We localized this region and its extension by fitting the X-ray pulse profile as observed by the NICER, NuSTAR, and RXTE telescopes in the ranges of 2–7 keV, 3–10 keV, and 9.4–22.4 keV, respectively.Results. We constrained the non-thermal X-ray emission to arise from altitudes between 0.2 rL and 0.55 rL where rL is the light-cylinder radius. The magnetic obliquity is approximately α ≈ 45° −50° and the LoS inclination angle is ζ ≈ 32° −48°.Conclusions. This Letter is among the first works to offer a tight constraint on the location of non-thermal X-ray emission from pulsars. We plan to apply this procedure to several other promising candidates to confirm this new result.