The invention relates to a device for treating the hair including a first and a second arm connected together by a joint and able to move with respect to one another between a closed configuration for treating the hair and a spread configuration for engaging between them the hairs to be treated. The device also includes a refill including a body having a housing, a member for applying a cosmetic product received in the housing. The refill includes at least one first mounting means engaging with at least one second mounting means of the first arm, in such a way that the assembly of the first and second mounting means is performed by moving the first mounting means along an axis (Y) substantially parallel to the joint, relative to the second mounting means.