This study explores the effects of carbon nanotube (CNT) orientation on stress transfer in carbon fiber (CF) composites using the Single Fiber Fragmentation Test (SFFT). A micromechanical hierarchical model, utilizing the Finite Element Method (FEM), is developed to analyze a CF composite with a CNT-reinforced interfacial region, encapsulated within an epoxy resin matrix. The Mori-Tanaka method is utilized to calculate the effective properties of the CNT-reinforced interfacial region of the CF, taking into account different CNT orientations and volume fractions. Scenarios involving radial, longitudinal, and random CNT orientations are considered. Moreover, the study also incorporates the nonlinear plastic behavior of the epoxy matrix. A novel analytical framework that leverages FEM to compute variables such as critical length, interfacial shear strength (IFSS), and average normal stress is proposed to accomplish it. Numerical results are compared to existing experimental data for validation. For the validation of the proposed methodology, experimental data available in the literature were used. The model predictions show that specific orientations and volume fractions of CNTs have the potential to enhance IFSS. However, the enhancement in the elastic stiffness of the interfacial region, attributed to the inclusion of CNTs, does not entirely explain the improvements in IFSS observed in the experimental studies from the literature.