Carbon nanotubes (CNT)-reinforced polymeric composites are being studied as promising materials due to their enhanced properties. However, understanding the behavior of polymers during non-isothermal crystallization is important once the degree of crystallinity and crystallization processes are affected when nanoparticles are added to matrices. Usually, crystallization kinetics studies are performed using a model-fitting method, though the isoconversional method allows to obtain the kinetics parameter without assuming a crystallization model. Therefore, in this work, CNTs were oxidized (CNT-Ox) and functionalized with gamma-aminobutyric acid (GABA) (CNT-GB) and incorporated into a poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) matrix. The influence of the addition and functionalization of CNT in the crystallization kinetics of PHBV was evaluated using the isoconversional method with differential scanning calorimetry (DSC), and by polarized light optical microscopy (PLOM) and Shore D hardness. The incorporation and functionalization of CNT into PHBV matrix did not change the Šesták and Berggren crystallization model; however, the lowest activation energy was obtained for the composite produced with CNT-GB, suggesting a better dispersion into the PHBV matrix. PLOM and Shore D hardness confirmed the results obtained in the kinetics study, showing the smallest crystallite size for CNT-containing nanocomposites and the highest hardness value for the composite produced with CNT-GB.