Steve Murrells, the Co-operative Group's chief executive, said it put a halt to the sale of single knives about three weeks ago.
"We've launched our 'safer colleague, safer community' campaign to support colleague safety and help identify the causes of community crime. This has seen us remove kitchen knives from sale in our stores," he said.
The increase in the number of fatal stabbings has prompted government action, including controversial plans to involve teachers in prevention, as well as making it easier for police to stop and search people.
The Co-op's move follows Asda, which last month said it would withdraw single kitchen knives from its stores. Single knives are the most commonly stolen knife products from stores, Asda said.
Between March 2017 and March 2018, there were 285 killings using a knife or sharp instrument in England and Wales - the highest number since Home Office records began in 1946. The number has risen four years in a row after a long-term decline.
The rise in knife crime has been most marked in areas outside London, according to Guardian analysis of official statistics.
In March, Philip Hammond, the chancellor, announced an extra £100m in funding for police forces in England and Wales over the course of the next year "to pay for additional overtime targeted specifically on knife crime".
Comment: Banning the sale of kitchen knives is like putting a band-aid on a gaping wound - a symbolic gesture at best. The causes of London's skyrocketing crime wave are varied and complex, and it will take a good deal more than banning the sale of knives to address the situation.