Visceral leishmaniasis is a parasitic disease that affects, among other areas, both sides of the Mediterranean Basin. The drugs classically used in clinical practice are pentavalent antimonials (SbV) and amphotericin B, which are nephrotoxic, require parenteral administration, and increasing drug resistance in visceral leishmaniasis has been observed. These circumstances justify the search of new families of compounds to find effective drugs against the disease. Eukaryotic type I DNA topoisomerase (TopIB) has been found essential for the viability of the parasites, and therefore represents a promising target in the development of an antileishmanial therapy. In this search, heterocyclic compounds, such as 1,5-naphthyridines, have been prepared by cycloaddition reaction between N-(3-pyridyl)aldimines and acetylenes and their antileishmanial activity on promastigotes and amastigote-infected splenocytes of Leishmania infantum has been evaluated. In addition, the cytotoxic effects of newly synthesized compounds were assessed on host murine splenocytes in order to calculate the corresponding selective indexes (SI). Excellent antileishmanial activity of 1,5-naphthyridine 19, 21, 22, 24 and 27 has been observed with similar activity than the standard drug amphotericin B and higher selective index (SI > 100) towards L. infantum amastigotes than amphotericin B (SI > 62.5). Special interest shows the 1,5-naphthyridine 22 with an IC50 value (0.58 ± 0.03 μM) similar to the standard drug amphotericin B (0.32 ± 0.05 μM) and with the highest selective index (SI = 271.5). In addition, this compound shows remarkable inhibition on leishmanial TopIB. However, despite these interesting results, further studies are needed to disclose other potential targets involved in the antileishmanial effect of these novel compounds.