We present 3.6-160 μm infrared images of Kepler's supernova remnant (SN 1604) obtained with the IRAC and MIPS instruments on the Spitzer Space Telescope. We also present MIPS SED low-resolution spectra in the 55-95 μm region. The observed emission in the MIPS 24 μm band shows the entire shell. Emission in the MIPS 70 μm and IRAC 8 μm bands is seen only from the brightest regions of 24 μm emission, which also correspond to the regions seen in optical Hα images. Shorter wavelength IRAC images are increasingly dominated by stars, although faint filaments are discernible. The SED spectrum of shows a faint continuum dropping off to longer wavelengths and confirms that strong line emission does not dominate the mid-IR spectral region. The emission we see is due primarily to warm dust emission from dust heated by the primary blast wave; no excess infrared emission is observed in regions where supernova ejecta are seen in X-rays. We use models of the dust to interpret the observed 70/24 μm ratio and constrain the allowed range of temperatures and densities. We estimate the current mass of dust in the warm dust component to be 5.4 × 10-4 M☉, and infer an original mass of about 3 × 10-3 M☉ before grain sputtering. The MIPS 160 μm band shows no emission belonging to the remnant. We place a conservative but temperature-dependent upper limit on any cold dust component roughly a factor of 10 below the cold dust mass inferred from SCUBA observations. Finally, we comment on issues relevant to the possible precursor star and the supernova type.