Moiré superlattices have recently been extensively studied in both electronic and photonic systems, e.g., magic-angle bilayer graphene showing superconductivity and twisted bilayer photonic crystals leading to magic-angle lasers. However, the moiré physics is barely studied in the field of magnonics, i.e., in using spin waves for information processing. In this work, we report magnon flat-band formation in twisted bilayer magnonic crystals at the optimal "magic angle" and interlayer exchange coupling combination using micro magnetic simulations. At the flat-band frequency, magnons undergo a strong two-dimensional confinement with a lateral scale of about 185 nm. The magic-angle magnonic nanocavity occurs at the AB stacking region of a moiré unit cell, unlike its photonic counterpart which is at the AA region, due to the exchange-induced magnon spin torque. The magnon flat band originates from band structure reformation induced by interlayer magnon-magnon coupling. Our results enable efficient accumulation of magnon intensity in a confined region that is key for potential applications such as magnon Bose-Einstein condensation and even magnon lasing.