We have carried out VLA Zeeman observations of H I absorption lines toward the H 11 region in the M17 giant molecular cloud complex. The resulting maps have 60" x 45" spatial resolution and 0.64 km s(-1) velocity separation. The H I absorption lines toward M17 show between 5 and 8 distinct velocity components, which vary spatially in a complex manner across the source. We explore possible physical connections between these components and the M17 region based on calculations of H I column densities, line-of-sight magnetic field strengths, as well as comparisons with a wide array of previous optical, infrared, and radio observations. In particular, an H I component at the same velocity as the southwestern molecular cloud (M17 SW; similar to 20 km s(-1)) seems to originate from the edge-on interface between the H II region and M17 SW in unshocked photodissociation region (PDR) gas. We have detected a steep enhancement in the 20 km s(-1) H I column density and line-of-sight magnetic field strengths (B-los) toward this boundary. A lower limit for the peak 20 km s(-1) H I column density is N-HI/T-s greater than or equal to 5.6 x 10(19) cm(-2) K-1, whereas the peak B-los is similar to -450 mu G. In addition, blended components at velocities of 11-17 km s(-1) appear to originate from shocked gas in the PDR between the H II region and an extension of M17 SW, which partially obscures the southern bar of the H II region. The peak N-HI/T-s and B-los for this component are greater than or equal to 4.4 x 10(19) cm(-2) K-1 and similar to +550 mu G, respectively. Comparison of the peak magnetic fields detected toward M17 with virial equilibrium calculations suggest that approximate to 1/2 of M17 SW's total support comes from its static magnetic energy, while the other half of its support is supplied by the turbulent kinetic energy (including MHD waves).