We have observed the decoherence of a lithium atomic wave during its propagation in the presence of the radiation emitted by tungsten-halogen lamps, i.e., decoherence induced by blackbody radiation. We used our atom interferometer to detect this decoherence by measuring the atom fringe-visibility loss. The absorption of a photon excites the atom, which spontaneously emits a fluorescence photon. The momenta of these two photons have random directions, and this random character is the main source of decoherence. All previous similar experiments used small-bandwidth coherent excitation by a laser, whereas incoherent radiation involves several technical and conceptual differences. Our approach is interesting as blackbody radiation is omnipresent and decoherence should be considered if particles resonant to electromagnetic fields are used.