Where appropriate, it will replace the devices - which emit a high-pitched sound audible only to the under-20s - with a system that plays classical music.
The Mosquito was being used in a number of former United Co-operative stores in the North West and Yorkshire. A spokeswoman for The Co-operative Group said that no new ones had been installed since last year, when United Co-operatives was merged into the group.
The move comes just a month after Sir Albert Aynsley-Green, the children's commissioner for England, suggested that the device discriminated against young people.
The Co-operative Group's decision will come as a blow to many c-store retailers who believe the devices to be an invaluable tool in their fight against antisocial behaviour.