The apparatus for measurement of a current which is flowing in an axially elongated electrical conductor at a first electrical potential. The apparatus contains at least one associated sensor element associated with the conductor that is electrically isolated from it at a second electrical potential different from the first electrical potential of the electrical conductor, and having magnetoresistive characteristics. The sensor element is intended to form a loop which is magnetically closed around the conductor in the circumferential direction, with the resistance value being tapped off at axially opposite ends. Its magnetoresistive part is preferably composed of a non-metallic powder composite material with a high magnetoresistive effect.