Burns are a common health problem worldwide and are highly susceptible to bacterial infections that are difficult to handle with ordinary wound dressings. Therefore, burn wound repair is extremely challenging in clinical practice. Herein, a series of self-healing hydrogels (QCS/OD/TOB/PPY@PDA) with good electrical conductivity and antioxidant activity were prepared on the basis of quaternized chitosan (QCS), oxidized dextran (OD), tobramycin (TOB), and polydopamine-coated polypyrrole nanowires (PPY@PDA NWs). These Schiff base cross-links between the aminoglycoside antibiotic TOB and OD enable TOB to be slowly released and responsive to pH. Interestingly, the acidic substances during the bacteria growth process can induce the on-demand release of TOB, avoiding the abuse of antibiotics. The antibacterial results showed that the QCS/OD/TOB/PPY@PDA9 hydrogel could kill high concentrations of Pseudomonas aeruginosa (PA), Staphylococcus aureus, and Escherichia coli in a short time and showed a bactericidal effect for up to 11 days in an agar plate diffusion experiment, while showing good in vivo antibacterial activity. Excellent and long-lasting antibacterial properties make it suitable for severely infected wounds. Furthermore, the incorporation of PPY@PDA endowed the hydrogel with near-infrared (NIR) irradiation assisted bactericidal activity of drug-resistant bacteria, conductivity, and antioxidant activity. Most importantly, in the PA-infected burn wound model, the QCS/OD/TOB/PPY@PDA9 hydrogel more effectively controlled wound inflammation levels and promoted collagen deposition, vascular generation, and earlier wound closure compared to Tegaderm dressings. Therefore, the TOB smart release hydrogels with on-demand delivery are extremely advantageous for bacterial-infected burn wound healing.