We report a detection of the 9.7 micrometer silicate absorption feature in a damped Lyman-alpha (DLA) system at z_{abs} = 0.524 toward AO0235+164, using the Infrared Spectrograph (IRS) onboard the Spitzer Space Telescope. The feature shows a broad shallow profile over about 8-12 micrometers in the absorber rest frame and appears to be > 15 sigma significant in equivalent width. The feature is fit reasonably well by the silicate absorption profiles for laboratory amorphous olivine or diffuse Galactic interstellar clouds. To our knowledge, this is the first indication of 9.7 micrometer silicate absorption in a DLA. We discuss potential implications of this finding for the nature of the dust in quasar absorbers. Although the feature is relatively shallow (tau_{9.7} = 0.08-0.09), it is about 2 times deeper than expected from extrapolation of the tau_{9.7} vs. E(B-V) relation known for diffuse Galactic interstellar clouds. Further studies of the 9.7 micrometer silicate feature in quasar absorbers will open a new window on the dust in distant galaxies.