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Magnetic field processing is promising for directing and enhancing self-assembly of diamagnetic block copolymers (BCPs) via domain alignment, but is typically limited to high field strengths and few polymer chemistries. Herein, a novel magnetic field-induced ordering mechanism distinct from domain alignment is demonstrated in aqueous, spherical BCP micelles. Here, low-intensity magnetic fields (B< 0.5 T) induce an anomalous disorder-to-order transition, accompanied by a several order-of-magnitude increase in shear modulus-- effectively transforming a low viscosity liquid into an ordered soft solid. The induced moduli are orders of magnitude larger than those resulting from thermally-induced ordering. Further magnetization induces cubic-to-cylinder order-to-order transitions. Comprehensive characterization via magnetorheology, small- and wide-angle X-ray scattering, differential scanning calorimetry, and vibrational spectroscopy reveals a significant reduction in micelle size and aggregation number relative to zero-field temperature- or concentration-induced ordering, suggesting that B-fields strongly alter polymer-solvent interactions. This extraordinary BCP ordering strategy enables discovery of structures and d-spacings inaccessible via traditional processing routes, thus providing a new platform for developing advanced materials with precisely-controlled features.