Bionanocomposites of poly(3-hydroxybutyrate–co-3-hydroxyvalerate) (PHBV) reinforced with PHBV-grafted multi-walled carbon nanotubes (PHBV-g-MWCNTs) were prepared through a simple solution casting method. The obtained nanocomposite films containing 1–10 wt.% PHBV-g-MWCNTs were transparent in the visible wavelength range. In addition, the PHBV-g-MWCNTs were uniformly dispersed throughout the PHBV matrix and thus improved the thermal stability and mechanical, barrier, and migration properties of PHBV. Compared to neat PHBV, the tensile strength and Young’s modulus of the nanocomposite film containing 7 wt.% PHBV-g-MWCNTs were enhanced by 88% and 172%, respectively, and the maximum decomposition temperature of the nanocomposite film was 22.3°C greater than that of neat PHBV. Moreover, the nanocomposites exhibited a wider melt-processing window and reduced water uptake and water vapor permeability. Furthermore, the migration levels of simulants in all of the nanocomposites were below the overall migration limits required by current legislative standards for food packaging materials in both non-polar and polar simulants.