We present near-infrared spectroscopy of fluorescent molecular hydrogen (H-2) emission from molecular filaments in the reflection nebula NGC 7023. We derive the relative column densities of H-2 rotational-vibrational states from the measured line emission and compare these results with several model photodissociation regions covering a range of densities, incident UV fields, and excitation mechanisms. Our best-fit models for one filament suggest, but do not require, either a combination of different densities, suggesting clumps of 10(6) cm(-3) in a 10(4)-10(5) cm(-3) filament, or a combination of fluorescent excitation and thermally excited gas, perhaps due to a shock from a bipolar outflow. We derive densities and UV fields for these molecular filaments that are in agreement with previous determinations.