We present differential radial velocity measurements of Proxima Centauri collected over 4 years with the ESO CES with a mean precision of 54 ms(-1) . We find no evidence of a periodic signal that could corroborate the existence of a sub-stellar companion. We put upper limits (97% confidence) to the companion mass ranging from 1.1 to 22 M_Jup at orbital periods of 0.75 to 3000 d, i.e. separations 0.008-2 AU from Prox Cen. Our mass limits concur with limits found by precise astrometry (Benedict et al. 1998a and priv. comm.) which strongly constrain the period range 50-600 d to 1.1-0.22 M_Jup. Combining both results we exclude a brown dwarf or supermassive planet at separations 0.008-0.69 AU from Prox Cen. We also find that, at the level of our precision, the RV data are not affected by stellar activity. Based on observations collected at the European Southern Observatory, La Silla.