Fabry-Perot images of the H-2 1-0 S(1) emission line in Herbig-Haro 7-11 have been obtained with a velocity resolution of 25 km s-1 and a spatial resolution of 1.2. The H-2 line profiles peak at lower (absolute) radial velocity than the atomic lines and have smaller line widths (FWHM). However, the H-2 profiles have weak high-velocity wings, and the full width at zero intensity velocities are similar to those of the atomic lines. In the vicinity of HH 11, the velocity extent of the H-2 emission is greater than 200 km s-1. It is suggested that the weak emission ncar HH 11 may be produced by H-2 reformation pumping in fast shocks and that the extremely high velocity CO observed in the same region could have a similar ofigin. The H-2 emission in HH 7 has the velocity field expected for a Tadiating bow shock, with strong H-2 emission at the apex of the bow shock. It is suggested that the H-2 emission from HH 7 consists of two components: (1) a magnetic precursor in a high-velocity (approximately 100 km s-1) J-shock which produces most of the H-2 emission, and (2) a postshock component that is responsible for the weak high-velocity emission. The postshock component could be reformation pumping or emission from H-2 that has survived dissociation in the shock front. A theoretical bow shock with a simple parameterized model for the magnetic precursor is presented to explain the observed velocity field in HH 7. J-shocks with magnetic precursors are the most attractive explanation for the combined optical and infrared data, although detailed theoretical calculations of such shocks are required.