We report the detection of infrared emission from the jet of the nearby Fanaroff-Riley type I radio galaxy 3C 31. The jet was detected with the IRAC instrument on Spitzer at 4.5 μm, 5.8 μm, and 8.0 μm out to 30'' (13 kpc) from the nucleus. We measure radio, infrared, optical, and X-ray fluxes in three regions along the jet determined by the infrared and X-ray morphology. Radio through X-ray spectra in these regions demonstrate that the emission can be interpreted as synchrotron emission from a broken power-law distribution of electron energies. We find significant differences in the high-energy spectra with increasing distance from the nucleus. Specifically, the high-energy slope increases from 0.86 to 1.72 from 1 kpc to 12 kpc along the jet, and the spectral break likewise increases in frequency along the jet from tens to hundreds of GHz to ~20 THz. Thus, the ratio of IR-to-X-ray flux in the jet increases by at least an order of magnitude with increasing distance from the nucleus. We argue that these changes cannot simply be the result of spectral aging and that there is ongoing particle acceleration through this region of the jet. The effects of mass loading, turbulence, and jet deceleration, however these processes modify the jet flow in detail, must be causing a change in the electron energy distribution and the efficiency of particle acceleration.