Zn‐air batteries (ZABs) offer promising commercialization perspectives for stretchable and wearable electronic devices as they are environment‐friendly and have high theoretical energy density. However, current devices suffer from limited energy efficiency and durability because of the sluggish oxygen reduction and evolution reactions kinetics in the air cathode as well as degenerative stretchability of solid‐state electrolytes under highly alkaline conditions. Herein, excellent bifunctional catalytic activity and cycling stability is achieved by using a newly developed Co–N–C nanomaterial with a uniform virus‐like structure, prepared via a facile carbonization of a prussian blue analogue (PBA). Furthermore, a solid‐state dual‐network sodium polyacrylate and cellulose (PANa‐cellulose) based hydrogel electrolyte is synthesized with good alkaline‐tolerant stretchability. A solid‐state fiber‐shaped ZAB fabricated using this hydrogel electrolyte, the virus‐like Co–N–Cs air cathode, and a zinc spring anode display excellent stretchability of up to 500% strain without damage, and outstanding electrochemical performance with 128 mW cm−2 peak power density and good cycling stability for >600 cycles at 2 mA. The facile synthesis strategy demonstrated here opens up a new avenue for developing highly active PBA‐derived catalyst and shows, for the first time, that virus‐like structure can be favorable for electrochemical performance.