The antibacterial efficacy and specificity of lytic bacteriophages (phages) make them promising therapeutics for treatment of multidrug-resistant bacterial infections. Restricted penetration of phages through the protective matrix of biofilms, however, may limit their efficacy against biofilm infections. Here, engineered polymers were used to generate noncovalent phage-polymer nanoassemblies (PPNs) that penetrate bacterial biofilms and kill resident bacteria. Phage K, active against multiple strains of Staphylococcus aureus, including methicillin-resistant S. aureus (MRSA), was assembled with cationic poly(oxanorbornene) polymers into PPNs. The PPNs retained phage infectivity, while demonstrating enhanced biofilm penetration and killing relative to free phages. PPNs achieved 3-log10 bacterial reduction (∼99.9%) against MRSA biofilms in vitro. PPNs were then incorporated into Poloxamer 407 (P407) hydrogels and applied onto in vivo wound biofilms, demonstrating controlled and sustained release. Hydrogel-incorporated PPNs were effective in a murine MRSA wound biofilm model, showing a 1.5-log10 reduction in bacterial load compared to a 0.5 log reduction with phage K in P407 hydrogel. Overall, this work showcases the therapeutic potential of phage K engineered with cationic polymers for treating wound biofilm infections.