The leishmaniases are vector-borne parasitic diseases affecting humans and animals, with high mortality rates in endemic countries. Infected dogs represent the main reservoir of infection. Disease control is mainly based on chemotherapy, which, at present, shows serious drawbacks both in humans and dogs. Therefore, the discovery or repurposing of new treatments is mandatory. Here, three monovalent ionophores (salinomycin, monensin, nigericin) were tested against promastigotes of Leishmania (L.) infantum, Leishmania tropica, and Leishmania braziliensis, and against amastigotes of L. infantum within human and, for the first time, canine macrophages. All three drugs were leishmanicidal against all Leishmania spp. promastigotes with IC50 values between 7.98 and 0.23 µM. Monensin and nigericin showed IC50 values < 1 µM, whereas salinomycin was the least active compound (IC50 > 4 µM). Notably, the ionophores killed L. infantum amastigotes within human THP-1 cells with IC50 values ranging from 1.67 to 1.93 µM, but they only reduced by 27–37% the parasite burden in L. infantum-infected canine macrophages, showing a host-specific efficacy. Moreover, a selective higher toxicity against canine macrophages was observed. Overall, repurposed ionophores have the potential to be further investigated as anti-Leishmania agents, but different drug options may be required to tackle human or canine leishmaniases.