The new bread bags should degrade within four years, compared to the 100-year plus life of a traditional polythene bag.
The bags will rot away into small organic residue, carbon dioxide and water.
The Co-op has also brought in biodegradable bags for shoppers to pack their purchases in, according to newspaper reports.
The retailer decided to use degradable wrapping for its bread following a survey which indicated that consumers would prefer retailers to use degradable or biodegradable materials.
The company estimated that 10,521 tonnes of waste are generated by bread bags every year.