The sensitive detection of sound waves is essential for a variety of applications. In this work, we propose a miniature diaphragm-free fiber-optic microphone based on a plano-concave optical micro-interferometer. A solid plano-concave micro-interferometer is formed at the end of a cleaved fiber by depositing a tiny volume of liquefied glass. Sound wave induced periodic variation of pressure can significantly modify the refractive index of the plano-concave glass due to the elasto-optic effect, and then, the phase difference between two interferometric beams will be remarkably changed accordingly. The interferometer finally converts the fluctuation of the phase difference into the change in the output optical power. Consequently, the sound wave can be demodulated by detecting the output power of the microphone. The experimental results show that the proposed microphone has the ability to detect sound waves in the whole audible range and almost omnidirectional. The noise-limited minimum detectable sound pressure is around 12 µPa/Hz. In addition, the human voice detection test shows that the performance of our microphone is competitive with the most advanced commercial device. The structure is stable without any movable mechanical parts, and the size is as small as 0.25 mm, which makes the proposed microphone an attractive alternative to the conventional one for sound wave detection.