The use of natural bioactive molecules, such as curcumin, has become increasingly popular in wound healing due to its antibacterial and antioxidant properties. However, the low solubility of curcumin has limited its applications. To overcome this issue, starch-derived cyclodextrin, such as hydroxypropyl-γ-cyclodextrin (CD), has been utilized to encapsulate curcumin and enhance its solubility. In this study, inclusion complexes of curcumin (Cur) and hydroxypropyl-γ-cyclodextrin (CD/Cur) were coated onto non-woven cotton fabrics to gain the fast-release property. The citric acid (CA) was used as a cross-linking reagent to form poly-CD, in which poly-CD/Cur structure can provide a slow release of curcumin. The optimized solutions (CD/Cur and poly-CD/Cur) can generate the nanofibers (NF) and nanobeads (NB), by using electrospinning and electrospraying methods, respectively, which were collected onto the nonwoven-cotton substrate. Time-dependent in vitro release test demonstrated that the CD/Cur has improved the solubility of curcumin in an aqueous environment and has fast release ability, while the cross-linked poly-CD/Cur exhibited slow-release characteristics, particularly in a weakly acidic environment. The NF structures showed higher release and maximum release percentages of curcumin compared to the NB structures. In vitro, antioxidant assays also demonstrated that both NF and NB samples exhibited excellent antioxidant activity, poly-CD/Cur and CD/Cur, illustrating slow and fast free radical scavenging effects, respectively. In summary, the poly-CD/Cur nanostructures with nonwoven-cotton substrates have excellent slow-controlled release ability, and CD/Cur nanostructures show excellent fast-release ability. All samples have the potential as a wound healing biomaterial due to the unique properties of curcumin, cyclodextrin, and their nanostructures.