A high-sensitivity low-frequency fiber optic hydrophone based on weak value amplification (WVA) is proposed and demonstrated. A polarization maintaining (PM) fiber with a length of 0.8 m wound around a polycarbonate (PC) tube is used as the sensing element. Theoretical analysis shows that the PM fiber in a WVA measurement scheme responds to underwater acoustic pressure with unprecedented sensitivity. The prototypical hydrophone based on such a scheme can sense underwater acoustic disturbance as weak as 1.3×10−6 Pa/Hz1/2 at 10 Hz, with a flat frequency response in the low-frequency band of 0.1–50 Hz. The experimental result agrees well with the theoretical prediction to within 0.5 dB.