We report a miniaturized fiber inline Fabry-Perot interferometer (FPI), with an open micro-notch cavity fabricated by one-step fs laser micromachining, for highly sensitive refractive index measurement. The device was tested for measurement of the refractive indices of various liquids including isopropanol, acetone and methanol at room temperature, as well as the temperature-dependent refractive index of deionized water from 3 to 90 degrees C. The sensitivity for measurement of refractive index change of water was 1163 nm/RIU at the wavelength of 1550 nm. The temperature cross-sensitivity of the device was about 1.1x10(-6) RIU/degrees C. The small size, all-fiber structure, small temperature dependence, linear response and high sensitivity, make the device attractive for chemical and biological sensing.