Use of drug-carrying scaffolds in regenerative medicine induces simultaneous tissue regeneration and drug release at the injury site. In this research, nanofibrous scaffolds based on poly-caprolactone/decellularized Wharton’s jelly matrix (PCL/DWJM) with a weight ratio of 20:80 containing curcumin were prepared through electrospinning method. Nanofibrous scaffolds were then compared in terms of morphology, physicochemical properties, and drug release in the presence and absence of MWCNTs-COOH. The morphology of the fibers, observed using a Scanning Electron Microscope (SEM), shows that the presence of curcumin and MWCNT increases the conductivity of the solution and charge density as well, thereby reducing the diameter of nanofibers and facilitating the electrospinning process. Infrared Spectroscopy (FTIR) indicated the interaction between the functional groups in curcumin, DWJM, and MWCNT, hence an improvement in the tensile strength of the scaffold. Addition of MWCNT-COOH increased the tensile strength of the scaffold by about two times that of the scaffold without ceramics. Curcumin, as a lipophilic substance in the PCL/DWJM structure, prevents the reduction of the contact angle while addition of MWCNT-COOH decreases the contact angle of water. The drug release evaluation revealed that compared to the polymer scaffold without ceramics, the amount of curcumin released from the scaffold containing MWCNT-COOH enhanced due to the increased repulsion of the negative charges between the oxygen anion and carboxylate anion.