The ultrafast transfer of excitation energy from one atom to its neighbor is observed in singly charged argon dimers in a time-resolved extreme ultraviolet (XUV)-pump IR-probe experiment. In the pump step, bound 3s-hole states in the dimer are populated by single XUV-photon ionization. The excitation-energy transfer at avoided crossings of the potential-energy curves leads to dissociation of the dimer, which is experimentally observed by further ionization with a time-delayed IR-probe pulse. From the measured pump-probe delay-dependent kinetic-energy release of coincident Ar+ + Ar+ ions, we conclude that the transfer of energy occurs on a time scale of about 800fs. This mechanism represents a fast relaxation process below the energy threshold for interatomic Coulombic decay.