It has been proposed that the stellar cores observed in ultra-faint dwarf (UFD) galaxies reflect underlying dark matter (DM) cores that cannot be formed by stellar feedback acting on collisionless cold dark matter (CDM) halos. Assuming this claim is correct, we investigate the constraints that arise if such cores are produced by self-interacting dark matter (SIDM). We derive the range of SIDM cross sections (σ/m) required to reproduce the observed core sizes. These can result from halos in either the core-formation phase (low σ/m) or the core-collapse phase (high σ/m), yielding a wide range of allowed values (∼0.3─200 cm2 g−1) consistent with those reported in the literature for more massive galaxies. We also construct a simple model that relates stellar mass to core radius ─ two observables likely connected in SIDM. This model reproduces the stellar core sizes and masses in UFDs with σ/m values consistent with the above range. It also predicts a trend of increasing core radius with stellar mass, in agreement with observations of more massive dwarf galaxies. The model's central DM densities match observations when assuming that the SIDM profile originates from an initial CDM halo that follows the mass─concentration relation. Since stellar feedback is insufficient to form cores in these galaxies, UFDs unbiasedly anchor σ/m at low velocities. If the core-collapse scenario holds (i.e., high σ/m), UFD halos are thermalized on kiloparsec scales, approximately two orders of magnitude larger than the stellar cores. These large thermalization scales could potentially influence substructure formation in more massive systems.