Recent advances in additive manufacturing have led to the development of innovative solutions for tissue regeneration. Hydrogel materials have gained significant attention for burn wound treatment in clinical practice among various advanced dressings due to their soothing and moisturizing activity. However, prolonged healing, pain, and traumatic removal due to the lack of long-term wound hydration are some of the challenges in the treatment of second-degree burn wounds. In this study, 3D-printed dressings were fabricated using gelatin, alginate, and bioactive borate glass (BBG) using an extrusion-based bioprinter. After ionic crosslinking, the 3D-printed dressings were characterized for mechanical properties, degradation rate, hydration activity, and in vitro cell viability using human fibroblasts. The results demonstrated that in 3D-printed dressings with 20 wt% BBG, Young’s modulus increased by 105%, and 10-day degradation rate decreased by 62%. Addition of BBG prevented the burst release of water from hydrogel dressings and enabled the continuous water release for up to 10 days, which is crucial in treating second-degree burn wounds. 3D-printed hydrogel dressings with BBG showed long-term cell viability that can be a result of the accumulative release of therapeutic ions from BBG particulate. The in vivo wound healing functionality of the dressings was investigated using a rat model with a second-degree burn wound. Our animal study showed that the 3D-printed dressings with BBG exhibited faster wound closure, non-adhesive contact, non-invasive debridement, and non-traumatic dressing removal. Histological analysis suggested that 3D-printed dressings contributed to more uniform re-epithelialization and tissue remodeling compared to the non-printed hydrogels of the same compositions. Critically, 3D-printed dressings with BBG led to significant regeneration of hair follicles compared to the 3D-printed hydrogel, non-printed hydrogel, and the control groups. The superior outcome of the 3D-printed hydrogel–BBG20 dressings can be attributed to the bioactive formulation, which promotes moist wound healing for longer time periods, and the non-adhesive porous texture of the 3D-printed dressings with increased wound-dressing interactions. Our findings provided proof of concept for the synergistic effect of bioactive formulation and the porous texture of the 3D-printed hydrogel dressings incorporated with BBG on continuous water release and, consequently, on second-degree burn wound healing.