Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes and known as non-reciprocal charge transport. The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems. Here, we probe the ultimate limits of miniaturization by creating atomic-scale Pb--Pb Josephson junctions in a scanning tunneling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behavior, confirming the high quality of the junctions, but no asymmetry between the bias directions. Non-reciprocal supercurrents emerge when inserting a single magnetic atom into the junction, with the preferred direction depending on the atomic species. Aided by theoretical modelling, we trace the non-reciprocity to quasiparticle currents flowing via electron-hole asymmetric Yu-Shiba-Rusinov (YSR) states inside the superconducting energy gap and identify a new mechanism for diode behavior in Josephson junctions. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation.