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We present the first polarized dust emission measurements of the Horsehead Nebula, obtained using the POL-2 polarimeter on the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) camera on the James Clerk Maxwell Telescope (JCMT). The Horsehead Nebula contains two sub-millimeter sources, a photodissociation region (PDR; SMM1) and a starless core (SMM2). We see well-ordered magnetic fields in both sources. We estimated plane-of-sky magnetic field strengths of 56$\pm$9 and 129$\pm$21 $\mu$G in SMM1 and SMM2, respectively, and obtained mass-to-flux ratios and Alfv\'en Mach numbers of less than 0.6, suggesting that the magnetic field can resist gravitational collapse and that magnetic pressure exceeds internal turbulent pressure in these sources. In SMM2, the kinetic and gravitational energies are comparable to one another, but less than the magnetic energy. We suggest a schematic view of the overall magnetic field structure in the Horsehead Nebula. Magnetic field lines in SMM1 appear have been compressed and reordered during the formation of the PDR, while the likely more-embedded SMM2 may have inherited its field from that of the pre-shock molecular cloud. The magnetic fields appear to currently play an important role in supporting both sources., Comment: Accepted to the Astronomical Journal