A multiplexed and spatially-resolved optical fiber tip sensor is proposed and demonstrated for multi-point refractive index (RI) sensing based on a microwave-photonic interrogation technique. The RI sensor is simply based on an array of cleaved end facets of optical fibers with different lengths fabricated from off-the-shelf optical fiber couplers. An auxiliary optical fiber endface that serves as the reference reflector is also introduced into the system. As a result, each of the sensing reflectors from the sensor array, together with the reference reflector, forms a Michelson interferometer (MI). Interrogated by a microwave-photonic system operating at an incoherent regime, the interferogram for each of the MIs in the microwave domain can be unambiguously reconstructed. The spatial location and ambient RI of the sensing reflector can be determined based on the free spectral range and magnitude at the resonance of the microwave interferogram. An analytical model is first developed to understand the physics of the sensor, followed by a proof-of-concept demonstration. Two sensing reflectors and a reference reflector are multiplexed in the prototype system, showing high RI sensitivity and low temperature crosstalk. The unique features of the sensor, such as ease of fabrication, low cost, high sensitivity, low temperature dependence, multiplexing and spatially-resolved capabilities, make the sensor a strong candidate for biochemical and environmental sensing applications.