There is a great interest in developing drug delivery systems that are biocompatible and release the drug in a controlled way. In this study, the release of curcumin from electrospun meshes made from polycaprolactone, polylactic acid, or their blends was studied and compared. The polymers and curcumin were dissolved in a mixture of chloroform and dimethylformamide. The beadless electrospun meshes were obtained under the following conditions: the applied voltage of 22 kV, the tip to collector distance of 13 cm, and the polymer feed rate of 0.2 ml/h. The viscosity of the polymer solution increased by increasing the percentage of polylactic acid in the mixture. As a result, the average fiber diameter of the meshes was increased. The fabricated polycaprolactone mesh showed the minimum average fiber diameter (∼120 nm) and the maximum porosity (∼71%). The hybrid nanofibrous meshes were also fabricated using two counter nozzles on both sides of the collector. The tensile strengths of the polylactic acid and polycaprolactone electrospun meshes loaded with curcumin were 19.86 and 12.64 MPa, respectively. The tensile strain of the meshes increased from 43 to 116% by increasing the polycaprolactone weight percentage in the mixture. The results showed that the physical–mechanical properties of the fabricated electrospun meshes could be tuned by polymer blending. The release of curcumin from these electrospun meshes was monitored in a buffer solution using an UV-Vis spectrophotometer. The critical parameters on the release of curcumin were found to be the type of polymers, the average diameter of nanofibers, porosity, and hydrophilicity of the meshes.