A brake pedal module for a brake-by-wire brake system of a vehicle is disclosed, having a carrier component for securing the brake pedal module on the vehicle, a brake pedal pivotably mounted on the carrier component, and a damping unit for producing a resistance during actuation of the brake pedal. The damping unit has an insert, which comprises at least one elastic element. A receptacle for the insert is formed on the carrier component, which receptacle forms a housing of the damping unit and into which the insert is inserted.