Context: PKS 0903-57 is a little-studied gamma-ray blazar which has recently attracted considerable interest due to the strong flaring episodes observed since 2020 in HE (100 MeV < E < 100 GeV) and VHE (100 GeV < E < 10 TeV) gamma-rays. Its nature and properties are still not well determined. In particular, it is unclear whether PKS 0903-57 is a BL Lac or a Flat Spectrum Radio Quasar (FSRQ), while its redshift estimation relies on a possibly misassociated low signal-to-noise spectrum. Aim: We aim to reliably measure the redshift of the blazar and to determine its spectral type and luminosity in the optical range. Methods: We performed spectroscopy of the optical counterpart of the blazar using the South African Large Telescope (SALT) and the Very Large Telescope (VLT) and monitored it photometrically with the Rapid Eye Mount (REM) telescope. Results: We firmly measured the redshift of the blazar as z= 0.2621 +/- 0.0006 thanks to the detection of five narrow optical lines. The detection of a symmetric broad Halpha line with Full Width at Half Maximum (FWHM) of 4020 +/- 30 km/s together with a jet-dominated continuum leads us to classify it as a FSRQ. Finally, we detected with high significance a redshift offset (about 1500 km/s) between the broad line and the host. This is the first time that such an offset is unequivocally detected in a VHE blazar, possibly pointing to a very peculiar accretion configuration, a merging system, or a recoiling Black Hole.