Organogels (ORGs) are semi-solid materials, in which an organic phase is immobilized by a three-dimensional network composed of self-organized system, forming the aqueous phase. In this context, lipid–Pluronics (PLs) ORGs form a two-phase system which can be effectively used as skin delivery systems, favoring their permeation across the skin. In this study, we presented the development of ORG skin drug-delivery systems for curcumin (CUR), a liposoluble phenolic pigment extracted from the turmeric rhizome. In special, we designed the formulation compositions in order to carry high amounts of CUR soluble in oleic acid (OA), as organic phase, entrapped into an aqueous phase composed of micellar PL-based hydrogels by associating two polymers with different hydrophilic–lipophilic balances, Pluronic F-127 (PL F-127), and Pluronic L-81 (PL L-81), to enhance the permeation across the skin. Results revealed that the incorporation of PL L-81 favored the CUR incorporation into micelle–micelle interface. CUR insertion into OA-PL F-127/L-81 reduced both G’/G” relationship (∼16 x) and viscosity values (η* ∼ 54 mPa.s, at 32.5°C), disturbing the ORG network structural organization. In vitro permeation assays through Strat-M® skin-model membranes showed that higher CUR-permeated amounts were obtained for OA-PL F-127/L-81 (4.83 µg.cm−2) compared to OA-PL F-127 (3.51 μg.cm−2) and OA (2.25 μg.cm−2) or hydrogels (∼1.2 μg.cm−2, p < 0.001). Additionally, ORG formulations presented low cytotoxic effects and evoked pronounced antileishmanial activity (IC50 < 1.25 µg.ml−1), suggesting their potential use as skin delivery systems against Leishmania amazonensis. Results from this study pointed out OA-PL-based ORGs as promising new formulations for possible CUR topical administration.