Structural transitions of host systems in response to guest binding dominate many chemical processes. We report an unprecedented type of structural flexibility within a meta-rigid material, MFM-520, which exhibits a reversible periodic-to-aperiodic structural transition resulting from a drastic distortion of a [ZnO₄N] node controlled by the specific host-guest interactions. The aperiodic crystal structure of MFM-520 has no three-dimensional (3D) lattice periodicity but shows translational symmetry in higher-dimensional (3 + 2)D space. We have directly visualized the aperiodic state which is induced by incommensurate modulation of the periodic framework of MFM-520·H₂O upon dehydration to give MFM-520. Filling MFM-520 with CO₂ and SO₂ reveals that, while CO₂ has a minimal structural influence, SO₂ can further modulate the structure incommensurately. MFM-520 shows exceptional selectivity for SO₂ under flue-gas desulfurization conditions, and the facile release of captured SO₂ from MFM-520 enabled the conversion to valuable sulfonamide products. MFM-520 can thus be used as a highly efficient capture and delivery system for SO₂.