By means of zoom-in hydrodynamic simulations, we quantify the amount of neutral hydrogen (H i) hosted by groups and clusters of galaxies. Our simulations, which are based on an improved formulation of smoothed particle hydrodynamics, include radiative cooling, star formation, metal enrichment and supernova feedback, and can be split into two different groups, depending on whether feedback from active galactic nuclei (AGN) is turned on or off. Simulations are analysed to account for H I self-shielding and the presence of molecular hydrogen. We find that the mass in neutral hydrogen of dark matter haloes monotonically increases with the halo mass and can be well described by a power law of the form MH I(M, Z)∝ M3/4. Our results point out that AGN feedback reduces both the total halo mass and its H i mass, although it is more efficient in removing H i. We conclude that AGN feedback reduces the neutral hydrogen mass of a given halo by ~50 per cent, with a weak dependence on halo mass and redshift. The spatial distribution of neutral hydrogen within haloes is also affected by AGN feedback, whose effect is to decrease the fraction of H i that resides in the halo inner regions. By extrapolating our results to haloes not resolved in our simulations, we derive astrophysical implications from the measurements of ΩH I(Z): haloes with circular velocities larger than ~25 km s-1 are needed to host H i in order to reproduce observations. We find that only the model with AGN feedback is capable of reproducing the value of ΩHIbHI derived from available 21 cm intensity mapping observations.Fil: Villaescusa-Navarro, Francisco. Istituto Nazionale di Astrofisica; Italia. Istituto Nazionale di Fisica Nucleare; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Planelles, Susana. Universidad de Valencia; España. Università degli Studi di Trieste; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Borgani, Stefano. Istituto Nazionale di Astrofisica; Italia. Istituto Nazionale di Fisica Nucleare; Italia. Università degli Studi di Trieste; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Viel, Matteo. Istituto Nazionale di Astrofisica; Italia. Istituto Nazionale di Fisica Nucleare; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Rasia, Elena. Istituto Nazionale di Astrofisica; Italia. University of Michigan; Estados Unidos. Consiglio Nazionale delle Ricerche; ItaliaFil: Murante, Giuseppe. Istituto Nazionale di Astrofisica; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Dolag, Klaus. Universitäts-Sternwarte München; Alemania. Gobierno de la República Federal de Alemania. Max Planck Institut für Astrophysik; AlemaniaFil: Steinborn, Lisa K.. Universitäts-Sternwarte München; AlemaniaFil: Biffi, Veronica. Istituto Nazionale di Astrofisica; Italia. Università degli Studi di Trieste; Italia. Consiglio Nazionale delle Ricerche; ItaliaFil: Beck, Alexander M.. Universitäts-Sternwarte München; AlemaniaFil: Ragone Figueroa, Cinthia Judith. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina