In order to create new biodegradable nanocomposites for biomedicine, packaging, and environmentally effective adsorbents, ultra-thin composite fibers consisting of poly(3-hydroxybutyrate) (PHB) and graphene oxide (GO) were obtained by electrospinning. Comprehensive studies of ultrathin fibers combining thermal characteristics, dynamic electron paramagnetic resonance (ESR) probe measurements, and scanning electron microscopy (SEM) were carried out. It is shown that at the addition of 0.05, 0.1, 0.3, and 1% OG, the morphology and geometry of the fibers and their thermal and dynamic characteristics depend on the composite content. The features of the crystalline and amorphous structure of the PHB fibers were investigated by the ESR and DSC methods. For all compositions of PHB/GO, a nonlinear dependence of the correlation time of molecular mobility TEMPO probe (τ) and enthalpy of biopolyether melting (ΔH) is observed. The influence of external factors on the structural-dynamic properties of the composite fiber, such as hydrothermal exposure of samples in aqueous medium at 70 °C and ozonolysis, leads to extreme dependencies of τ and ΔH, which reflect two processes affecting the structure in opposite ways. The plasticizing effect of water leads to thermal destruction of the orientation of the pass-through chains in the amorphous regions of PHB and a subsequent decrease in the crystalline phase, and the aggregation of GO nanoplates into associates, reducing the number of GO-macromolecule contacts, thus increasing segmental mobility, as confirmed by decreasing τ values. The obtained PHB/GO fibrillar composites should find application in the future for the creation of new therapeutic and packaging systems with improved biocompatibility and high-barrier properties.