The recent discovery of an earth-like planet around Proxima Centauri has drawn much attention to this star and its environment. We performed a series of observations of Proxima Centauri using Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE), the planet-finder instrument installed at the European Southern Observatory (ESO) Very Large Telescope (VLT) UT3, using its near-infrared modules, InfraRed Dual-band Imager and Spectrograph (IRDIS) and IFS. No planet was detected directly, but we set upper limits on the mass up to 7 au by exploiting the AMES-COND models. Our IFS observations reveal that no planet more massive than similar to 6-7 M-Jup can be present within 1 au. The dual-band imaging camera IRDIS also enables us to probe larger separations than other techniques such as radial velocity or astrometry. We obtained mass limits of the order of 4 M-Jup at separations of 2 au or larger, representing the most stringent mass limits at separations larger than 5 au available at the moment. We also made an attempt to estimate the radius of possible planets around Proxima using the reflected light. Since the residual noise for the observations is dominated by photon noise and thermal background, longer exposures in good observing conditions could improve the achievable contrast limit further.