Aims. We investigate the dependence of galaxy clustering on luminosity and stellar mass in the redshift range 0.5 < z < 1.1, using the first 55 000 redshifts from the VIMOS Public Extragalactic Redshift Survey (VIPERS). Methods. We measured the redshift-space two-point correlation functions (2PCF), (s) and  , and the projected correlation function, , in samples covering different ranges of B-band absolute magnitudes and stellar masses. We considered both threshold and binned galaxy samples, with median B-band absolute magnitudes - 21.6 and median stellar masses . We assessed the real-space clustering in the data from the projected correlation function, which we model as a power law in the range  . Finally, we estimated the galaxy bias as a function of luminosity, stellar mass, and redshift, assuming a flat cold dark matter model to derive the dark matter 2PCF. Results. We provide the best-fit parameters of the power-law model assumed for the real-space 2PCF – the correlation length, , and the slope, – as well as the linear bias parameter, as a function of the B-band absolute magnitude, stellar mass, and redshift. We confirm and provide the tightest constraints on the dependence of clustering on luminosity at 0.5 < z < 1.1. We prove the complexity of comparing the clustering dependence on stellar mass from samples that are originally flux-limited and discuss the possible origin of the observed discrepancies. Overall, our measurements provide stronger constraints on galaxy formation models, which are now required to match, in addition to local observations, the clustering evolution measured by VIPERS galaxies between z = 0.5 and z = 1.1 for a broad range of luminosities and stellar masses.