Caffeic acid and related natural compounds were previously described as Leishmania amazonensis arginase (L-ARG) inhibitors, and against the whole parasite in vitro. In this study, we tested cinnamides that were previously synthesized to target human arginase. The compound caffeic acid phenethyl amide (CAPA), a weak inhibitor of human arginase (IC50 = 60.3 ± 7.8 μM) was found to have 9-fold more potency against L-ARG (IC50 = 6.9 ± 0.7 μM). The other compounds that did not inhibit human arginase were characterized as L-ARG, showing an IC50 between 1.3–17.8 μM, and where the most active was compound 15 (IC50 = 1.3 ± 0.1 μM). All compounds were also tested against L. amazonensis promastigotes, and only the compound CAPA showed an inhibitory activity (IC50 = 80 μM). In addition, in an attempt to gain an insight into the mechanism of competitive L-ARG inhibitors, and their selectivity over mammalian enzymes, we performed an extensive computational investigation, to provide the basis for the selective inhibition of L-ARG for this series of compounds. In conclusion, our results indicated that the compounds based on cinnamoyl or 3,4-hydroxy cinnamoyl moiety could be a promising starting point for the design of potential antileishmanial drugs based on selective L-ARG inhibitors.