Emission from vibrationally excited H2 has been discovered which is associated with the bright optical shock-excited filaments to the northeast of the Cygnus Loop supernova remnant. Infrared spectroscopy and infrared and optical narrow-band images of the shock-excited gas have been obtained in an effort to understand the mechanism of H2 excitation. A shock model with a magnetic precursor is proposed which explains quantitatively the observed H2 surface brightness, level population, and relation to optical emission. A shock with a magnetic precursor can also account for some of the anomalous properties of nonradiative shocks. 64 refs.