Conventional approaches to the high-power laser radiation measurement are thermal and photoelectric techniques. These methods require deflection of part of laser radiation power for its energy conversion into heat or electrical current, respectively. However, application of the beam splitters leads to significant distortion of laser beams. This limits the usability of these techniques for continuous measurement during the laser operation in industrial processes. In this study, a novel technique of fiber laser power measurement is presented. We have used a sensor representing a segment of single-mode optical fiber with copper coating. When laser radiation was transmitted through the copper-coated silica fiber sensor, its small part was scattered mainly due to Rayleigh scattering and therefore absorbed by the outer layer. This led to fiber heating and hence to the electrical resistance change of its metal layer, which was measured by milliohm meter.