The application prospects of fiber optic Mach-Zehnder interferometer (MZI) acousto-sensing technology in the field of partial discharge (PD) detection are promising. However, current external fiber optic sensors are not sensitive enough to effectively detect PDs. There is an urgent need to increase sensor sensitivity. In this article, a power-function-curved mandrel sensor (PMS) with an acoustic wave enhancement function was developed, and a fiber MZI acoustic wave sensing system was built. Based on the standard sinusoidal signal, the amplitude and frequency response characteristics of the sensor were measured, and the influence of the mandrel curved surface length on the system sensitivity was studied. The results show that the PMS possesses enhanced acousto-sensing effects. When driven by a piezoelectric transducer (PZT) emitting 40-kHz acoustic waves at 0.36 V, the PMS achieved the lowest detection threshold of the system, which is 0.44 V lower than that of the cylindrical mandrel sensor (CMS). In the 2-60-kHz frequency range, the sensitivity of the PMS is 41.0% higher than that of the CMS, with an average sensitivity increase of 50.4%. At low frequencies, the signal-to-noise ratio (SNR) of the sensor improves with an increase in the length of the mandrel curved surface. Finally, the effectiveness of the sensing system for detecting rod-rod electrode discharges was tested. It was found that the response peak-to-peak value of the PMS is higher than that of the CMS, proving that the acoustic sensing system can be used for external sensing of power equipment discharges.