Aims . As part of the Herschel guaranteed time key program ’ HOBYS ’ , we present the PACS and SPIRE photometric survey of the star forming region Vela-C , one of the nearest sites of low-to-high-mass star formation in the Galactic plane . Our main objectives are to take a census of the cold sources and to derive their mass distribution down to a few solar masses . Methods . Vela-C has been observed with PACS and SPIRE in parallel mode at five wavelengths between 70 \mu m and 500 \mu m over an area of about 3 square degrees . A photometric catalogue has been extracted from the detections in each of the five bands , using a threshold of 5 \sigma over the local background . Out of this catalogue we have selected a robust sub-sample of 268 sources , of which \sim 75 % are cloud clumps ( diameter between 0.05 pc and 0.13 pc ) and 25 % are cores ( diameter between 0.025 pc and 0.05 pc ) . Their Spectral Energy Distributions ( SEDs ) have been fitted with a modified black body function . We classify 48 sources as protostellar , based on their detection at 70 \mu m or at shorther wavelengths , and 218 as starless , because of non-detections at 70 \mu m. For two further sources , we do not provide a secure classification , but suggest they are Class 0 protostars . Results . From SED fitting we have derived key physical parameters ( i.e . mass , temperature , bolometric luminosity ) . Protostellar sources are in general warmer ( \langle T \rangle =12.8 K ) and more compact ( \langle diameter \rangle =0.040 pc ) than starless sources ( \langle T \rangle =10.3 K , \langle diameter \rangle =0.067 pc ) . Both these evidences can be ascribed to the presence of an internal source ( s ) of moderate heating , which also causes a temperature gradient and hence a more peaked intensity distribution . Moreover , the reduced dimensions of protostellar sources may indicate that they will not fragment further . A virial analysis of the starless sources gives an upper limit of 90 % for the sources gravitationally bound and therefore prestellar in nature . A luminosity vs. mass diagram of the two populations shows that protostellar sources are in the early accretion phase , while prestellar sources populate a region of the diagram where mass accretion has not started yet . We fit a power law N ( log M ) \propto M ^ { -1.1 \pm 0.2 } to the linear portion of the mass distribution of prestellar sources . This is in between that typical of CO clumps and those of cores in nearby star-forming regions . We interpret this as a result of the inhomogeneity of our sample , which is composed of comparable fractions of clumps and cores .