The retailer, which has 2,600 shops, said many people only used the 10p bags once before throwing them away.
The Co-op said its move would take 29.5 million bags for life, or about 870 tonnes of plastic, out of circulation every year. The Co-op said it would replace the plastic bags with compostable carrier bags selling for 10p "when current stocks are exhausted".
Co-op Food chief executive Jo Whitfield said the increased use of bags for life had led to a sharp rise in plastic use.
"With over 1.5 billion bags sold each year by retailers, this remains a massive issue for our industry as many shoppers are regularly buying so called 'Bags for Life' to use just once and it's leading to major hike in the amount of plastic being produced."
Earlier this month Morrisons said it would switch from offering plastic "bags for life" to a paper alternative.
Waitrose is currently trialling the removal of its 10p bags for life from a number of its stores with a view to rolling it out more widely.
Sainsbury's has said its bags for life cost 20p to encourage customers to re-use them and are made from 100% recycled plastic.
Asda has defended its continued use of plastic bags for life previously, saying they were a "sustainable alternative to single-use carrier bags... particularly given the concerns around CO2 emissions related to the paper-bag production process".