We report the design (in silico ADMET criteria), synthesis, cytotoxicity studies (HepG-2 cells), and biological evaluation of 15 hydrazine/hydrazide quinoxaline 1,4-di-N-oxide derivatives against the 3D7 chloroquine sensitive strain and FCR-3 multidrug resistant strain of Plasmodium falciparum and Leishmania infantum (axenic amastigotes). Fourteen of derivatives are novel quinoxaline 1,4-di-N-oxide derivatives. Compounds 18 (3D7 IC50 = 1.40 μM, FCR-3 IC50 = 2.56 μM) and 19 (3D7 IC50 = 0.24 μM, FCR-3 IC50 = 2.8 μM) were identified as the most active against P. falciparum, and they were the least cytotoxic (CC50-values > 241 μM) and most selective (SI > 86). None of the compounds tested against L. infantum were considered to be active. Additionally, the functional role of the hydrazine and hydrazide structures were studied in the quinoxaline 1,4-di-N-oxide system.