Context. The Fermi/LAT instrument has detected about two thousand extragalactic high energy (E ≥ 100 MeV) γ-ray sources. One of the brightest is 3FGL J1603.9-4903; it is associated to the radio source PMN J1603-4904. Its nature is not yet clear, it could be either a very peculiar BL Lac or a compact symmetric object radio source which are considered as the early stage of a radio galaxy. The latter, if confirmed, would be the first detection in γ-rays for this class of objects. A redshift z = 0.18 ± 0.01 has recently been claimed on the basis of the detection of a single X-ray line at 5.44 ± 0.05 keV which has been interpreted as a 6.4 keV (rest frame) fluorescent line. Aims. We aim to investigate the nature of 3FGL J1603.9-4903/PMN J1603-4904 using optical-to near-IR (NIR) spectroscopy. Methods. We observed PMN J1603-4904 with the UV-NIR VLT/X-Shooter spectrograph for two hours. We extracted spectra in the visible and NIR range that we calibrated in flux and corrected for telluric absorption. We systematically searched for absorption and emission features. Results. The source was detected starting from ~6300 Å down to 24 000 Å with an intensity similar to that of its 2MASS counterpart and a mostly featureless spectrum. The continuum lacks absorption features and thus is non-stellar in origin and most likely non-thermal. In addition to this spectrum, we detected three emission lines that we interpret as the Hα-[NII] complex, the [SII]λ,λ6716, 6731 doublet and the [SIII]λ 9530 line; we obtain a redshift estimate of z = 0.2321 ± 0.0004. The line ratios suggest that a LINER/Seyfert nucleus powers the emission. This new redshift measurement implies that the X-ray line previously detected should be interpreted as a 6.7 keV line which is very peculiar.