A series of biodegradable amphiphilic-block segmented polyurethanes (SPUs) are designed and synthesized based on di-block and tri-block macrodiols of polycaprolactone (PCL) and polyethylene glycol (PEG). Curcumin, as a model herbal antibacterial agent, is used due to its effective inhibitory action against Gram-positive and Gram-negative bacteria. Curcumin-loaded nanofibers, with 400-900 nm diameter range, have been prepared by electrospinning of SPUs. The synthesized SPUs can be used for wound dressing applications due to their excellent mechanical properties and higher hydrophilicity in comparison to PCL-based polyurethane. The elongation-at-break of tri-block SPU with PEG-PCL-PEG soft segments is 350% when produced as an electrospun mat and that for film is 1500%. In vitro release of curcumin, examined by UV-Vis spectroscopy, shows a steady release during 18 days. The inclusion of PEG chains in the soft segment increases the hydrophilicity and biodegradation rate of the electrospun mats compared to a PCL-based polyurethane, which eventually results in a higher curcumin release rate. The antibacterial activity of 50 mg of 10% curcumin-loaded SPU nanofibers is about 100% and 93% against Escherichia coli (E. coli ATCC: 25922) and Staphylococcus aureus (S. aureus ATCC: 6538), respectively. Nontoxic behavior of the scaffolds is evaluated through MTT assay against L929 mouse fibroblast cells. The results show that the synthesized SPUs can be used as a nanoscale sustained release carrier. The SPU with PEG-PCL-PEG soft segments is an excellent candidate for wound dressing in tissues undergoing large deformations during normal activities.