We have examined the relationship between the optical depth of the 9.7 micron silicate absorption feature (tau_9.7) and the near-infrared color excess, E(J-Ks) in the Serpens, Taurus, IC 5146, Chameleon I, Barnard 59, and Barnard 68 dense clouds/cores. Our data set, based largely on Spitzer IRS spectra, spans E(J-Ks)=0.3 to 10 mag (corresponding to visual extinction between about 2 and 60 mag.). All lines of sight show the 9.7 micron silicate feature. Unlike in the diffuse ISM where a tight linear correlation between the 9.7 micron silicate feature optical depth and the extinction (Av) is observed, we find that the silicate feature in dense clouds does not show a monotonic increase with extinction. Thus, in dense clouds, tau_9.7 is not a good measure of total dust column density. With few exceptions, the measured tau_9.7 values fall well below the diffuse ISM correlation line for E(J-Ks) > 2 mag (Av >12 mag). Grain growth via coagulation is a likely cause of this effect.