We report on the fabrication of a monolithic fiber Fabry-Perot interferometer whose cavity is a microscopic air bubble. The latter is formed when splicing together a conventional single-mode fiber and an index-guiding photonic crystal fiber with the standard arc-discharge technique. Spherical microcavities with diameters ranging from 20 to 58 microm were fabricated with such a technique. The interferometers exhibited low thermal sensitivity (less than 1.0 pm/ degrees C), high mechanical strength, broad operation wavelength range, and fringe contrast in the 8-12 dB range. The applications of the interferometers for strain sensing (up to 5000 micro(epsilon) is demonstrated.