ABSTRACT The recent data collected by Herschel have confirmed that interstellar structures with a filamentary shape are ubiquitously present in the Milky Way. Filaments are thought to be formed by several physical mechanisms acting from large Galactic scales down to subparsec fractions of molecular clouds, and they might represent a possible link between star formation and the large-scale structure of the Galaxy. In order to study this potential link, a statistically significant sample of filaments spread throughout the Galaxy is required. In this work, we present the first catalogue of 32 059 candidate filaments automatically identified in the Herschel Infrared Galactic plane Survey (Hi-GAL) of the entire Galactic plane. For these objects, we determined morphological (length la and geometrical shape) and physical (average column density $N_{\rm H_{2}}$ and average temperature T) properties. We identified filaments with a wide range of properties: 2 ≤ la ≤ 100 arcmin, $10^{20} \le N_{\rm H_{2}} \le 10^{23}$ cm−2 and 10 ≤ T ≤ 35 K. We discuss their association with the Hi-GAL compact sources, finding that the most tenuous (and stable) structures do not host any major condensation. We also assign a distance to ∼18 400 filaments, for which we determine mass, physical size, stability conditions and Galactic distribution. When compared with the spiral arms structure, we find no significant difference between the physical properties of on-arm and inter-arm filaments. We compare our sample with previous studies, finding that our Hi-GAL filament catalogue represents a significant extension in terms of Galactic coverage and sensitivity. This catalogue represents a unique and important tool for future studies devoted to understanding the filament life-cycle.