Context. Multiwavelength observations have revealed the highly unusual properties of the -ray source PMN J1603-4904, which are difficult to reconcile with any other well-established -ray source class. The object is either a very atypical blazar or a compact jet source seen at a larger angle to the line of sight. Aims: To determine the physical origin of the high-energy emission processes in PMN J1603-4904, we study the X-ray spectrum in detail. Methods: We performed quasi-simultaneous X-ray observations with XMM-Newton and Suzaku in 2013 September. This resulted in the first high signal-to-noise X-ray spectrum of this source. Results: The 2-10 keV X-ray spectrum can be well described by an absorbed power law with an emission line at 5.44 0.05 keV (observed frame). We interpret this feature as a K line from neutral iron and accordingly determine the redshift of PMN J1603-4904 to be z = 0.18 0.01, which corresponds to a luminosity distance of 872 54 Mpc. Conclusions: The detection of a redshifted X-ray emission line further challenges the original BL Lac classification of PMN J1603-4904. This result suggests that the source is observed at a larger angle to the line of sight than expected for blazars, and thus the source would add to the elusive class of -ray loud misaligned-jet objects, possibly a -ray bright young radio galaxy.