We present Spitzer measurements of the aromatic (also known as PAH) features for 35 Seyfert galaxies from the revised Shapley-Ames sample and find that the relative strengths of the features differ significantly from those observed in star-forming galaxies. Specifically, the features at 6.2, 7.7, and 8.6 micron are suppressed relative to the 11.3 micron feature in Seyferts. Furthermore, we find an anti-correlation between the L(7.7 micron)/L(11.3 micron) ratio and the strength of the rotational H2 (molecular hydrogen) emission, which traces shocked gas. This suggests that shocks suppress the short-wavelength features by modifying the structure of the aromatic molecules or destroying the smallest grains. Most Seyfert nuclei fall on the relationship between aromatic emission and [Ne II] emission for star-forming galaxies, indicating that aromatic-based estimates of the star-formation rate in AGN host galaxies are generally reasonable. For the outliers from this relationship, which have small L(7.7 micron)/L(11.3 micron) ratios and strong H2 emission, the 11.3 micron feature still provides a valid measure of the star-formation rate.