In this work, oleogels of cocoa butter (CB), rice bran oil (RBO), and graphene oxide (GO) were prepared. The prepared oleogels were subjected to various characterization techniques such as bright-field microscopy, X-ray diffraction (XRD), crystallization kinetics, differential scanning calorimetry (DSC), and mechanical studies. The influence of increasing GO content on the in vitro drug release and ex vivo corneal permeation of the model drug (ciprofloxacin HCl—CPH) from the oleogels was also investigated. Bright-field micrographs showed that increment in GO content reduced the size of the globular particles of CB. XRD analysis revealed that CB was crystallized in its β’ and β polymorphic forms in the oleogels, which was in agreement with thermal studies. The mechanical characterization demonstrated that the presence of GO improved the elastic nature and stress-bearing properties of the oleogels. Moreover, GO altered the crystallization kinetics of CB in the oleogels in a composition-dependent manner. The in vitro release of CPH from the oleogels occurred through either Fickian diffusion or fat network relaxation or a combination thereof. Furthermore, the inclusion of GO enhanced the ex vivo permeation of CPH molecules across the caprine cornea. Hence, we concluded that the prepared oleogels could be explored as potential delivery systems for ophthalmic applications.