Microbeam radiation therapy is a novel pre-clinical external beam therapy that uses high-brilliance synchrotron X-rays to deliver the necessary high dose rates. The unique conditions of high dose rate and high spatial fractionation demand a new class of detector to experimentally measure important beam quality parameters. Here we demonstrate the highest spatial resolution plastic scintillator fibre-optic dosimeter found in the literature to date and tested it on the Imaging and Medical Beam-Line at the Australian Synchrotron in a X-ray beam where the irradiation dose rate was 4435 Gy/s. With a one-dimensional spatial resolution of 10 μm the detector is able to resolve the individual microbeams (53.7 ± 0.4 μm wide), and measure the peak-to-valley dose ratio to be 55 ± 17. We also investigate the role of radioluminescence in the optical fibre used to transport the scintillation photons, and conclude that it creates a significant contribution to the total light detected.