A novel fiber-optic interferometric sensor is presented for vibrations measurements and analysis. In this approach, it is shown applied to the vibrations of electrical structures within power transformers. A main feature of the sensor is that an unambiguous optical phase measurement is performed using the direct detection of the interferometer output, without external modulation, for a more compact and stable implementation. High resolution of the interferometric measurement is obtained with this technique (<1 nm). The optical-fiber transducer is also specifically designed for magnifying the localized vibrations in order to modulate deeply the interferometric signal. Other advantages of the implementation for measurements within transformers are also highlighted.