A device for connecting an injector for an exhaust system in an internal combustion engine; said exhaust system comprises an exhaust duct and a connection pipe, which laterally protrudes from the exhaust duct; the connection device comprises: a tubular support body, which is provided with a longitudinal symmetry axis, is made of a thermally conductive material, is adapted to accommodate the injector therein, and at a lower end thereof, is adapted to be coupled to the connection pipe; an upper portion of the support body, which is suitable to be thermally coupled to an upper portion of a nose of the injector, so that a high heat exchange occurs between the upper portion of the nose of the injector and the upper portion of the support body; a lower portion of the support body, which is suitable to be thermally insulated from a lower portion of the nose of the injector, so that a low heat exchange occurs by conduction between the lower portion of the nose of the injector and the lower portion of the support body; the support body comprises a heat dissipation device, provided with a plurality of radial dissipation fins which are coaxial to the longitudinal symmetry axis, project outwards from the support body, and have the function of increasing the heat exchange surface; the connection device is characterized in that it further comprises a device for damping the vibrations transmitted to the heat dissipation device, which comprises, in turn, elastic elements coaxial to the longitudinal symmetry axis and accommodated at the lower portion of the support body; the elastic elements comprise a pair of plates which face each other and are both coaxial to the longitudinal symmetry axis so as to define an upper plate (27*) and a lower plate (27*), and wherein the elastic elements project outwards from the support body and their outer diameter substantially approximates the outer diameter of the plurality of radial dissipation fins. a tubular support body, which is provided with a longitudinal symmetry axis, is made of a thermally conductive material, is adapted to accommodate the injector therein, and at a lower end thereof, is adapted to be coupled to the connection pipe; an upper portion of the support body, which is suitable to be thermally coupled to an upper portion of a nose of the injector, so that a high heat exchange occurs between the upper portion of the nose of the injector and the upper portion of the support body; a lower portion of the support body, which is suitable to be thermally insulated from a lower portion of the nose of the injector, so that a low heat exchange occurs by conduction between the lower portion of the nose of the injector and the lower portion of the support body; the support body comprises a heat dissipation device, provided with a plurality of radial dissipation fins which are coaxial to the longitudinal symmetry axis, project outwards from the support body, and have the function of increasing the heat exchange surface; the connection device is characterized in that it further comprises a device for damping the vibrations transmitted to the heat dissipation device, which comprises, in turn, elastic elements coaxial to the longitudinal symmetry axis and accommodated at the lower portion of the support body; the elastic elements comprise a pair of plates which face each other and are both coaxial to the longitudinal symmetry axis so as to define an upper plate (27*) and a lower plate (27*), and wherein the elastic elements project outwards from the support body and their outer diameter substantially approximates the outer diameter of the plurality of radial dissipation fins.