We developed and experimented at sea an innovative fiber optic hydrophone (FOH) capable of operating at very low frequency of the seismic spectrum and for detecting small magnitude earthquakes. The FOH exploits an optical fiber coil wrapped around a sensitive mandrel in a Michelson interferometric configuration. The FOH operated for about seven days at a water depth of 40 m, in the Campi Flegrei volcanic area (Southern Italy), a few meters from a well calibrated PZT hydrophone used as a reference. Thirty-three local earthquakes occurred during the simultaneous operation of the two hydrophones, allowing a straightforward comparison of the recordings. The local earthquakes occurred at an epicentral distance shorter than 2.5 km from the site of recording, and were estimated to be in the range of magnitude from -0.8 to 2.7. The analysis of the recorded earthquake waveforms in the frequency and time domain allowed retrieving the response function of the FOH in the frequency range from 5 to 70 Hz. The FOH responsivity in terms of acoustic pressure reaches about 230 nm/Pa and is flat in the studied frequency range. The high quality of the FOH recordings make this equipment suitable for applications addressing submarine volcanic activity and the background seismicity of active faults in the ocean.