Ion irradiation can significantly change material properties. Thermal conductivity degradation of reactor fuel is detrimental to safety and efficiency—driving research on how irradiation impacts heat-carrying phonons. Here, we report the measurements of phonon dispersion and lifetimes (inverse linewidths) in freestanding irradiated crystals and reveal the relationship between thermal conductivity and proton irradiation induced nanostructures in UZr2.6 using inelastic x-ray scattering, electron microscopy, modulated thermoreflectance, and first-principles calculations. Irradiation results in more significant increases in phonon linewidths and decreased thermal conductivity in the basal plane than that along the c axis, decreasing thermal conductivity anisotropy. Microscopy reveals that this results from irradiation induced nanoprecipitates and metastable phase separation. Surprisingly, irradiation leads to smaller phonon linewidths near some zone boundaries, which we attribute to irradiation induced short-range order.