We report the first detection of the Zeeman effect in the 36 GHz Class I CH₃OH maser line. The observations were carried out with 13 antennas of the EVLA toward the high mass star-forming region M8E. Based on our adopted Zeeman splitting factor of z = 1.7 Hz mG^-1, we detect a line-of-sight magnetic field of –31.3 ± 3.5 mG and 20.2 ± 3.5 mG to the northwest and southeast of the maser line peak, respectively. This change in sign over a 1300 AU size scale may indicate that the masers are tracing two regions with different fields, or that the same field curves across the regions where the masers are being excited. The detected fields are not significantly different from the magnetic fields detected in the 6.7 GHz Class II CH₃OH maser line, indicating that CH₃OH masers may trace the large-scale magnetic field, or that the magnetic field remains unchanged during the early evolution of star-forming regions. Given what is known about the densities at which 36 GHz CH₃OH masers are excited, we find that the magnetic field is dynamically significant in the star-forming region.