A brake actuator is disclosed for an electromechanical vehicle brake, comprising an electric motor for actuating the vehicle brake, a blocking assembly for selectively rotationally blocking an output shaft of the electric motor for the purposes of implementing a parking brake function. The blocking assembly comprises a blocking module, which is mounted so as to be movable linearly between an arresting position and a release position, and a drive for moving the blocking module. The brake actuator further includes an electronic detection device for detecting the arresting position and/or the release position of the blocking module. Also specified is a method for operating a brake actuator.