Infrasound detection is important in natural disasters monitoring, military defense, underwater acoustic detection, and other domains. Fiber-optic Fabry–Perot (FP) acoustic sensors have the advantages of small structure size, long-distance detection, immunity to electromagnetic interference, and so on. The size of an FP sensor depends on the transducer diaphragm size and the back cavity volume. However, a small transducer diaphragm size means a low sensitivity. Moreover, a small back cavity volume will increase the low cut-off frequency of the sensor. Hence, it is difficult for fiber-optic FP infrasound sensors to simultaneously achieve miniaturization, high sensitivity, and extremely low detectable frequency. In this work, we proposed and demonstrated a miniaturized and highly sensitive fiber-optic FP sensor for mHz infrasound detection by exploiting a Cr-Ag-Au composite acoustic-optic transducer diaphragm and a MEMS technique-based spiral micro-flow hole. The use of the spiral micro-flow hole as the connecting hole greatly reduced the volume of the sensor and decreased the low-frequency limit, while the back cavity volume was not increased. Combined with the Cr-Ag-Au composite diaphragm, a detection sensitivity of $-123.19\mathrm{dB}\mathrm{re}1\mathrm{rad}/\mathrm{\mu Pa}$ at 5 Hz and a minimum detectable pressure (MDP) of $1.2\mathrm{mPa}/{\mathrm{Hz}}^{1/2}$ at 5 Hz were achieved. The low detectable frequency can reach 0.01 Hz and the flat response range was 0.01–2500 Hz with a sensitivity fluctuation of $\pm 1.5\mathrm{dB}$. Moreover, the size of the designed sensor was only $12\mathrm{mm}\times \mathrm{\Phi }12.7\mathrm{mm}$. These excellent characteristics make the sensor have great practical application prospects.