The main problem in power transformers is the degradation of the isolation, and partial discharges are a major contribution to this shortcoming. Partial discharges inside medium and high power transformers generate ultrasonic pressure waves which are detected, in this work, with an optical fibre interferometric sensor. The Mach-Zehnder interferometric sensor implemented, for the detection of partial discharges inside power transformers, is described. This sensor allows a high level sensitivity to be achieved for the typical small pressure variations created by partial discharges. Wavelet analysis is used to identify the acoustic patterns instead of more commonly used Fourier analysis. Acoustic signals contain numerous non-stationary or transitory characteristics that Fourier analysis does not allow them to be obtained: when transforming to frequency domain, temporal information disappears. It is possible to state when a particular event took place. The wavelet analysis helps to solve this problem. Some of the results of which are presented here. These results are compared to those obtained with piezoelectric acoustic sensors, when looking for the best wavelet application, showing good agreement between both methods. We have obtained clear signal between 15-17 kHz and, for the first time, wavelet analysis has provided a tool to identify the shape of the acoustic waves associated to partial discharges.