A low-frequency acoustic sensor based on fiber optic interferometer was designed and fabricated for detection of infrasound signals with a frequency less than 20 Hz. The sensor contains a metallic diaphragm that is a circular nickel membrane with a thickness of 5 μm and a radius of 1/2 inch (1 inch=2.54 cm), and the diaphragm is flatly fixed to a port of the metal cylinder in a peripherally stretched manner. The end face of the single-mode fiber protruding into the cylinder and the inner surface of the diaphragm constitute an extrinsic fiber Fabry-Perot interferometer (EFPI) for detecting the diaphragm's vibration caused by sound. In order to optimize the sensor performance, the effects of the prestress applied to the diaphragm and the diaphragm thickness on the first-order resonant frequency of the sensor are analyzed based on the principle of elastic mechanics and finite element simulation software. The simulation results show that the first-order resonant frequency is sensitive to prestress rather than to the diaphragm thickness under the condition of the diaphragm thickness being within a certain small range. The above-prepared fiber optic infrasound sensor was characterized with the B&K 4193-L-004 standard acoustic sensor and the 42AE standard infrasound source. The results show that the sensor has good frequency response in the range from 0.1 Hz to 20 Hz and the sensitivity to 1 Hz sound is as high as 285 mV/Pa.