Microresonators based on diverse material platforms have driven the progress of integrated photonics by enhancing light-matter interactions in compact volumes. Extending this strategy to magneto-optical (MO) media is highly attractive for nonreciprocal photonics, magnonics, and quantum transduction, yet compact high-Q resonators based on single-crystalline yttrium iron garnet (YIG) have remained elusive because of the difficulty of its nanofabrication. Here we demonstrate high-Q, small-mode-volume MO microdisk resonators based on monocrystalline Bi-substituted YIG (Bi:YIG). Low-loss Bi:YIG thin films prepared by bonding and thinning, combined with optimized Ar-plasma etching, enable submicron-thick, air-suspended microdisks that support telecom-band whispering-gallery modes with Q = 1.52× 10⁵, a mode volume V ≈ 200 cubic wavelengths, and Q/V ≈ 760, representing an orders-of-magnitude improvement for integrated high-Q YIG MO cavities. The device exhibits clear magnetic-field-dependent spectral responses, including reciprocal resonance shifts and nonreciprocal frequency splitting of counter-propagating modes. A perturbative analytical model quantitatively reproduces these responses and indicates an effective MO coefficient about twice the bulk value, suggesting a possible miniaturization-induced enhancement. These results establish monocrystalline YIG microdisks as a compact high-Q MO platform for integrated isolators, optomechanics, microcombs, and photon-magnon quantum interfaces.