Lead halide perovskite CsPbBr₃ is a wide-gap semiconductor material potentially very attractive for next generations of real-time monitors and particle detectors in high-energy physics. Here, we present the first characterization of crystalline CsPbBr₃ point dosimeters with submillimeter size, under 6 MV X-photon beams used in clinical radiotherapy. Current response of the devices proved to be promising in terms of fast rise and decay times, of the same order of the X-ray beam onset and offset ones; absence of polarization effects; reproducibility to repeated irradiations; and linearity of the collected charge as a function of the absorbed dose. Comparing the measured sensitivity with the theoretical one, a charge collection distance of about 100 μm has been evaluated, of the same order of the linear dimensions of crystallites within the samples, suggesting that recombination centers are mainly placed at grain boundaries. A much higher sensitivity per unit area measured with crystalline CsPbBr₃ as compared with drop-casted ones can be explained in terms of a less disordered crystalline structure. This work opens the way to CsPbBr₃ point dosimeters, with linear dimensions meeting the strict spatial resolution constraints for bidimensional dose mapping required in clinical radiotherapy.