An injection device for injecting a fluid into an exhaust-gas treatment device includes an injector positioned in an injector holder. The injector has a supply opening and a component of the injector holder extends into the supply opening. The injection device is suitable, in particular, for supplying a urea/water solution into an exhaust-gas treatment device of a motor vehicle. The component is preferably rigid in the longitudinal direction and can be compressed in the radial direction by way of a deformable rubber shell, in order to compensate for the volumetric expansion of the solution if it freezes. A motor vehicle having the injection device is also provided.