In this Paper we report on optical spectroscopic observations of the low-mass X-ray binary 2S 0921–630 obtained with the Very Large Telescope . We found sinusoidal radial velocity variations of the companion star with a semi–amplitude of 99.1 \pm 3.1 km s ^ { -1 } modulated on a period of 9.006 \pm 0.007 days , consistent with the orbital period found before for this source , and a systemic velocity of 44.4 \pm 2.4 km s ^ { -1 } . Due to X–ray irradiation the centre–of–light measured by the absorption lines from the companion star is likely shifted with respect to the centre–of–mass . We try to correct for this using the so–called K–correction . Conservatively applying the maximum correction possible and using the previously measured rotational velocity of the companion star , we find a lower limit to the mass of the compact object in 2S 0921–630 of M _ { X } \sin ^ { 3 } i > 1.90 \pm 0.25 M _ { \odot } ( 1 \sigma errors ) . The inclination in this system is well constrained since partial eclipses have been observed in X-rays and optical bands . For inclinations between 60 ^ { \circ } < i < 90 ^ { \circ } we find 1.90 \pm 0.25 < M _ { X } < 2.9 \pm 0.4 M _ { \odot } . However , using this maximum K–correction we find that the ratio between the mass of the companion star and that of the compact object , q , is 1.32 \pm 0.37 implying super–Eddington mass transfer rates ; however , evidence for that has not been found in 2S 0921–630 . We conclude that the compact object in 2S 0921–630 is either a ( massive ) neutron star or a low–mass black hole .