  We report on mid-infrared imaging observations of the anomalous X-ray pulsars
(AXPs) 1E 1048.1-5937, 1RXS J170849-400910, and XTE J1810-197. The observations
were carried out at 4.5 and 8.0 microns with the Infrared Array Camera and at
24 microns with the Multiband Imaging Photometer on the Spitzer Space
Telescope. No mid-infrared counterparts were detected. As infrared emission
from AXPs may be related to their X-ray emission either via the magnetosphere
or via a dust disk, we compare the derived upper limits on the infrared/X-ray
flux ratios of the AXPs to the same ratio for 4U 0142+61, an AXP previously
detected in the mid-infrared range. The comparison indicates that our three
non-detections are consistent with their relatively low X-ray fluxes. For XTE
J1810-197, our upper limits set a constraint on its rising radio/millimeter
energy spectrum, suggesting a spectral break between 1.5$\times
10^{11}$--6$\times10^{13}$ Hz.
