Self-healing hydrogels have good mechanical strength, can endure greater external force, and have the ability to heal independently, resulting in a strong bond between the wound and the material. Bacterial biofilm infections are life-threatening. Clindamycin (Cly) can be produced in the form of a self-healing hydrogel preparation. It is noteworthy that the antibacterial self-healing hydrogels show great promise as a wound dressing for bacterial biofilm infection. In this study, we developed a polyvinyl alcohol/borax (PVA/B) self-healing hydrogel wound dressing that releases Cly. Four ratios of PVA, B, and Cly were used to make self-healing hydrogels: F1 (4%:0.8%:1%), F2 (4%:1.2%:1%), F3 (1.6%:1%), and F4 (4%:1.6%:0). The results showed that F4 had the best physicochemical properties, including a self-healing duration of 11.81 ± 0.34 min, swelling ratio of 85.99 ± 0.12%, pH value of 7.63 ± 0.32, and drug loading of 98.34 ± 11.47%. The B–O–C cross-linking between PVA and borax caused self-healing, according to FTIR spectra. The F4 formula had a more equal pore structure in the SEM image. The PVA/B-Cly self-healing hydrogel remained stable at 6 ± 2 °C for 28 days throughout the stability test. The Korsmeyer–Peppas model released Cly by Fickian diffusion. In biofilm-infected mouse wounds, PVA/B-Cly enhanced wound healing and re-epithelialization. Our results indicate that the PVA/B-Cly produced in this work has reliable physicochemical properties for biofilm-infected wound therapy.