The noise equivalent index of a magnetohydrodynamics (MHD) angular vibration sensor is a comprehensive evaluation of the scale factor and output noise in the bandwidth range. Specifically, lower output noise and a lower low-frequency cut-off frequency within the -3 dB range indicate better practical performance of the sensor. Due to the extremely low source impedance of the MHD angular vibration sensor, noise matching can be achieved by using transformer coupling, improving the signal-to-noise ratio and significantly reducing the output noise. In this paper, the optimal turn ratio is analyzed and the transformer complete noise output model is established. The introduction of a transformer can increase the low-frequency cutoff frequency of the sensor. At the same time, in practical applications, it is observed that the sensor′s internal leakage magnetic field affects the transformer core, substantially reducing its magnetization inductance. This, in turn, degrades the low-frequency performance and prevents the noise equivalent index from reaching the expected level. To address this issue, a segmented and arc-shaped magnetic shielding structure is proposed for the noise-matching transformer, tailored to the sensor′s unique structure that converts axial magnetic fields into radial magnetic fields. Within the limited spatial constraints of miniaturized sensors, this design effectively mitigates the impact of magnetic leakage on the transformer and enhances the uniformity of the magnetic field within the fluid region. The effect is verified through finite element simulations and experimental testing. This structure greatly improves the low-frequency performance of the sensor in practical applications and significantly optimizes the noise equivalent index. The experimental results show that the low cut-off frequency is reduced to below 2 Hz, the noise equivalent angular rate reaches 2.6 μrad/s RMS, and the noise equivalent angular position is reduced to 32 nrad RMS.