The contribution of the magnetic field to the formation of high-mass stars is poorly understood. We report the high angular resolution (similar to 0.'' 3, 870 au) map of the magnetic field projected on the plane of the sky (B POS) toward the high-mass star-forming region G333.46-0.16 (G333), obtained with the Atacama Large Millimeter/submillimeter Array at 1.2 mm as part of the Magnetic fields in Massive star-forming Regions survey. The B POS morphology found in this region is consistent with a canonical "hourglass" with an embedded flattened envelope in a perpendicular direction, which suggests a dynamically important field. This region is fragmented into two protostars that appear to be gravitationally bound in a stable binary system with a separation of similar to 1740 au. Interestingly, by analyzing H13CO+ (J = 3-2) line emission, we find no velocity gradient over the extent of the continuum, which is consistent with a strong field. We model the B POS, obtaining a marginally supercritical mass-to-flux ratio of 1.43, suggesting an initially strongly magnetized environment. Based on the Davis-Chandrasekhar-Fermi method, the magnetic field strength toward G333 is estimated to be 5.7 mG. The absence of strong rotation and outflows toward the central region of G333 suggests strong magnetic braking, consistent with a highly magnetized environment. Our study shows that despite being a strong regulator, the magnetic energy fails to prevent the process of fragmentation, as revealed by the formation of the two protostars in the central region.