The device allows the pain associated with the insertion of a needle of a syringe into the skin to be reduced. To do this, this device comprises a sleeve, which has a first rear portion to at least partially receive the syringe with the needle and a second front portion fitted with an end part, through which an opening passes for passage of the needle. A front face of the end part is intended to be applied with pressure against the skin of a person before insertion of the needle into the skin. This front face of the end part is arranged to receive an active substance for desensitizing the skin. The active substance can be applied to the skin at the instant the terminal part presses on the penetration site to desensitize the skin.
