Chronic wounds such as diabetic ulcers are a major complication in diabetes caused by hyperglycemia, prolonged inflammation, high oxidative stress, and bacterial bioburden. Bioactive biopolymers have been found to have a biological response in wound tissue microenvironments and are used for developing advanced tissue engineering strategies to enhance wound healing. These biopolymers possess innate bioactivity and are biodegradable, with favourable mechanical properties. However, their bioactivity is highly dependent on their structural properties, which need to be carefully considered while developing wound healing strategies. Biopolymers such as alginate, chitosan, hyaluronic acid, and collagen have previously been used in wound healing solutions but the modulation of structural/physico-chemical properties for differential bioactivity have not been the prime focus. Factors such as molecular weight, degree of polymerization, amino acid sequences, and hierarchical structures can have a spectrum of immunomodulatory, anti-bacterial, and anti-oxidant properties that could determine the fate of the wound. The current narrative review addresses the structure–function relationship in bioactive biopolymers for promoting healing in chronic wounds with emphasis on diabetic ulcers. This review highlights the need for characterization of the biopolymers under research while designing biomaterials to maximize the inherent bioactive potency for better tissue regeneration outcomes, especially in the context of diabetic ulcers.