The device has a sleeve including a rear portion (21) to partially receive a syringe with a needle (8) and a front portion (24) fitted with an end part (25), through which an opening (27) passes for passage of the needle. A front face (26) of the end part is intended to be applied with pressure against a skin (P) of a person before insertion of the needle into the skin. The front face of the end part is arranged to receive an active substance (31) for desensitizing the skin. The front face includes a cavity between the opening and a peripheral edge (28) of the end part. The active substance is an anesthetic substance in form of gel and a cooling substance.
