This article proposes solid-like systems from sunflower oil structured with a fibrillar network built by the assembly of 12-hydroxystearic acid (12-HSA), a gelator molecule for an oil phase. The resulting organogels were studied as oral controlled release formulations for a lipophilic drug, Efavirenz (EFV), dissolved in the oil. The effects of the gelator concentration on the thermal properties of the organogels were studied by Differential Scanning Calorimetry (DSC) and showed that drug incorporation did not change the sol–gel–sol transitions. The erosion and drug release kinetics from organogels under conventional (filling gelatin capsules) or multiparticulate (beads obtained by prilling) dosage forms were measured in simulated gastric and intestinal fluids. EFV release profiles were analyzed using model-dependent (curve-fitting) and independent approaches (Dissolution Efficiency DE). Korsmeyer–Peppas was the best fitting release kinetic model based on the goodness of fit, revealing a release mechanism from organogels loaded with EFV different from the simple drug diffusion release mechanism obtained from oily formulations. From organogels, EFV probably diffuses through an outer gel layer that erodes releasing oil droplets containing dissolved EFV into the aqueous medium.