We present and analyze observations of polarized dust emission at 850 μm toward the central 1 × 1 pc hub-filament structure of Monoceros R2 (Mon R2). The data are obtained with SCUBA-2/POL-2 on the James Clerk Maxwell Telescope (JCMT) as part of the B-fields in Star-forming Region Observations survey. The orientations of the magnetic field follow the spiral structure of Mon R2, which are well described by an axisymmetric magnetic field model. We estimate the turbulent component of the magnetic field using the angle difference between our observations and the best-fit model of the underlying large-scale mean magnetic field. This estimate is used to calculate the magnetic field strength using the Davis–Chandrasekhar–Fermi method, for which we also obtain the distribution of volume density and velocity dispersion using a column density map derived from Herschel data and the C18O (J = 3 - 2) data taken with HARP on the JCMT, respectively. We make maps of magnetic field strengths and mass-to-flux ratios, finding that magnetic field strengths vary from 0.02 to 3.64 mG with a mean value of 1.0 ± 0.06 mG, and the mean critical mass-to-flux ratio is 0.47 ± 0.02. Additionally, the mean Alfvén Mach number is 0.35 ± 0.01. This suggests that, in Mon R2, the magnetic fields provide resistance against large-scale gravitational collapse, and the magnetic pressure exceeds the turbulent pressure. We also investigate the properties of each filament in Mon R2. Most of the filaments are aligned along the magnetic field direction and are magnetically subcritical.