Appropriate selection of suitable materials and methods is essential for scaffolds fabrication in tissue engineering. The major challenge is to mimic the structure and functions of the extracellular matrix (ECM) of the native tissues. In this study, an optimized 3D structure containing poly(3-hydroxybutyrate) (P3HB), multiwalled carbon nanotubes (MCNTs) and curcumin (CUR) was created by electrospinning a novel biomimetic scaffold. CUR, a natural anti-inflammatory compound, has been selected as a bioactive component to increase the biocompatibility and reduce the potential inflammatory reaction of electrospun scaffolds. The presence of CUR in electrospun scaffolds was confirmed by H-1 NMR and Fourier-transform infrared spectroscopy (FTIR). Scanning electron microscopy (SEM) revealed highly interconnected porosity of the obtained 3D structures. Addition of up to 20 wt% CUR has enhanced mechanical properties of the scaffolds. CUR has also promoted in vitro bioactivity and hydrolytic degradation of the electrospun nanofibers. The developed P3HB-MCNT composite scaffolds containing 20 wt% of CUR revealed excellent in vitro cytocompatibility using mesenchymal stem cells and in vivo biocompatibility in rat animal model study. Importantly, the reduced inflammatory reaction in the rat model after 8 weeks of implantation has also been observed for scaffolds modified with CUR. Overall, newly developed P3HB-MCNTs-CUR electrospun scaffolds have demonstrated their high potential for tissue engineering applications.