The sandfly midgut and the human macrophage phagolysosome provide antagonistic metabolic niches for the endoparasite Leishmania to survive and populate. Although these environments fluctuate across developmental stages, the relative changes in both these environments across parasite generations might remain gradual. Such environmental restrictions might endow parasite metabolism with a choice of specific genotypic and phenotypic factors that can constrain enzyme evolution for successful adaptation to the host. With respect to the available cellular information for Leishmania species, for the first time, we measure the relative contribution of eight inter-correlated predictors related to codon usage, GC content, gene expression, gene length, multi-functionality, and flux-coupling potential of an enzyme on the evolutionary rates of singleton metabolic genes and further compare their effects across three Leishmania species. Our analysis reveals that codon adaptation, multi-functionality, and flux-coupling potential of an enzyme are independent contributors of enzyme evolutionary rates, which can together explain a large variation in enzyme evolutionary rates across species. We also hypothesize that a species-specific occurrence of duplicated genes in novel subcellular locations can create new flux routes through certain singleton flux-coupled enzymes, thereby constraining their evolution. A cross-species comparison revealed both common and species-specific genes whose evolutionary divergence was constrained by multiple independent factors. Out of these, previously known pharmacological targets and virulence factors in Leishmania were identified, suggesting their evolutionary reasons for being important survival factors to the parasite. All these results provide a fundamental understanding of the factors underlying adaptive strategies of the parasite, which can be further targeted.