Malodorous wounds have a detrimental effect on the patient's well‐being. A dressing combining the properties of hydrogels and activated carbon (AC) would be beneficial for the treatment of these wounds, controlling wound exudate while adsorbing malodor‐causing compounds. The present work involves the use of acrylate‐endcapped, urethane‐based precursors (AUPs) and methacrylated alginate (AlgMOD). AUPs are synthesized with a varying poly(ethylene glycol) backbone molar mass (2–20 kg mol−1) to tune mechanical and swelling properties, whereas methacrylated alginate, known for its hemostatic properties, enables chemical cross‐linking. Blends of AUP and AlgMOD with AC are processed into hydrogel sheets and electrospun membranes. The results indicate tunable mechanical (Young's moduli 0.03–0.63 MPa) and swelling properties (2.2–34.9 gwaterghydrogel−1) along with high gel fractions (>85%). The sheets are compared with commercial odor‐adsorbing dressings (Carbonet and Carboflex), enabling benchmarking. AUP sheets (8 and 10 kg mol−1) containing 0.5% w/w AC show strong adsorption (>90% after 24 h) of crystal violet. The obtained (core–shell AlgMOD/AUP) fibers are visualized using scanning and transmission electron microscopy. Indirect cell tests reveal the developed materials to be biocompatible. In conclusion, a hydrogel‐based odor‐adsorbing wound dressing is successfully synthesized and holds promise for malodorous wound healing. [ABSTRACT FROM AUTHOR]