We report measurements of reflectances of 90377 Sedna at λ > 2.5 μm using the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. Sedna orbits well beyond even the Kuiper Belt, with a perihelion distance of 76 AU, and is therefore very faint as viewed from Earth, despite its relatively large size. Previously published near-infrared spectra show possible signatures of CH4 and N2 at ~2.3 and ~2.15 μm, respectively. These and other ices also exhibit much stronger absorptions at λ > 2.5 μm, providing the motivation for the present work. We detected flux from Sedna at 3.6 and 4.5 μm, but not at 5.8 or 8.0 μm. The measured IRAC fluxes are converted to geometric albedos and combined with previous measurements of the visible and near-infrared spectra. Strong absorption at both 3.6 and 4.5 μm (relative to the 2.0-2.5 μm region) is readily apparent, confirming the presence of ices on the surface of Sedna. Spectral modeling of the full wavelength range (0.4-4.5 μm) provides further constraints. We find that CH4 is required to fit the new data points, but that these new data points can not be adequately described with models containing CH4 and N2 as the only ices. We suggest that H2O ice is also present. Several characteristics of the spectrum of Sedna suggest an absence of atmospheric volatile transport, in contrast to the large objects Eris and 2005 FY9.