In this study, chitosan and collagen (Ch: Col)-based materials containing curcumin (Cur) as a bioactive compound were developed for wound-healing purposes. The effects of incorporating curcumin and increasing its concentration on both the rheological properties of the formed solutions and the morphological and thermal properties of the three-dimensional scaffolds obtained from them were evaluated. Rheology showed that the presence of curcumin resulted in solutions with a solid-like behavior (G’ > G″), higher collagen denaturation temperatures, and higher viscosities, favoring their use as biomaterials for wound healing. A greater cross-linking effect was observed at higher curcumin concentrations, possibly between the amino groups from both polymers and the hydroxyl and keto groups from the polyphenol. Such cross-linking was responsible for the delay in the onset of degradation of the scaffolds by 5 °C, as revealed by thermogravimetric analysis. Moreover, the pore diameter distribution profile of the scaffolds changed with increasing curcumin concentration; a greater number of pores with diameters between 40 and 60 µm was observed for the scaffold with the highest curcumin content (50 mg), which would be the most suitable for the proposed application. Thus, the materials developed in this study are presented as promising biomaterials for their biological evaluation in tissue regeneration.