Context. We present our observations and analysis of SN 2020cxd, a low-luminosity (LL), long-lived Type IIP supernova (SN). This object is a clear outlier in the magnitude-limited SN sample recently presented by the Zwicky Transient Facility’s (ZTF) Bright Transient Survey. Aims. We demonstrate that SN 2020cxd is an additional member of the group of LL SNe and we discuss the rarity of LL SNe in the context of the ZTF survey. We consider how further studies of these faintest members of the core-collapse (CC) SN family might help improve the general understanding of the underlying initial mass function for stars that explode. Methods. We used optical light curves (LCs) from the ZTF in the gri bands and several epochs of ultraviolet data from the Neil Gehrels Swift observatory as well as a sequence of optical spectra. We constructed the colour curves and a bolometric LC. Then we compared the evolution of the ejecta velocity and black-body temperature for LL SNe as well as for typical Type II SNe. Furthermore, we adopted a Monte Carlo code that fits semi-analytic models to the LC of SN 2020cxd, which allows for the estimation of the physical parameters. Using our late-time nebular spectra, we also make a comparison against SN II spectral synthesis models from the literature to constrain the progenitor properties of SN 2020cxd. Results. The LCs of SN 2020cxd show a great similarity with those of LL SNe IIP in terms of luminosity, timescale, and colours. Also, the spectral evolution of SN 2020cxd is that of a Type IIP SN. The spectra show prominent and narrow P-Cygni lines, indicating low expansion velocities. This is one of the faintest LL SNe observed, with an absolute plateau magnitude of Mr = −14.5 mag and also one with the longest plateau lengths, with a duration of 118 days. Finally, the velocities measured from the nebular emission lines are among the lowest ever seen in a SN, with an intrinsic full width at half maximum value of 478 km s−1. The underluminous late-time exponential LC tail indicates that the mass of 56Ni ejected during the explosion is much smaller than the average of normal SNe IIP, we estimate M56Ni = 0.003 M⊙. The Monte Carlo fitting of the bolometric LC suggests that the progenitor of SN 2020cxd had a radius of R0 = 1.3 × 1013 cm, kinetic energy of Ekin = 4.3 × 1050 erg, and ejecta mass of Mej = 9.5 M⊙. From the bolometric LC, we estimated the total radiated energy Erad = 1.52 × 1048 erg. Using our late-time nebular spectra, we compared these results against SN II spectral synthesis models to constrain the progenitor zero-age main sequence mass and found that it is likely to be ≲15 M⊙. Conclusions. SN 2020cxd is a LL Type IIP SN. The inferred progenitor parameters and the features observed in the nebular spectrum favour a low-energy, Ni-poor, iron CC SN from a low-mass (∼12 M⊙) red supergiant.