The existence of ellipsoidal micelles in aqueous solution has been debated in the literature. Although a number of experimental studies suggest that certain surfactants form ellipsoidal micelles, many theoretical studies have claimed that micelles with an ellipsoidal shape cannot exist. To shed light on this topic, in this paper, we develop a curvature-corrected, molecular-thermodynamic model for the free energy of micellization of nonionic surfactant biaxial ellipsoidal micelles. We subsequently use this model to evaluate the feasibility of forming ellipsoidal micelles, compared to forming spherical, spherocylindrical, and discoidal micelles, and conclude that ellipsoidal micelles can exist in solution. Utilizing the model developed here, we also establish theoretical limits on the size of the ellipsoidal micelles. These limits depend solely on the chemical structure of the surfactant molecule.