We report the experimental observation of quantum interference in the nuclear wave-packet dynamics driving ultrafast excitation-energy transfer in argon dimers below the threshold of interatomic Coulombic decay (ICD). Using time-resolved photoion-photoion coincidence spectroscopy and quantum dynamics simulations, we reveal that the electronic relaxation dynamics of the inner-valence 3s hole on one atom leading to a 4s or 4p excitation on the other one is influenced by nuclear quantum dynamics in the initial state, giving rise to a deep, periodic modulation on the kinetic-energy-release (KER) spectra of the coincident Ar^{+}-Ar^{+} ion pairs. Moreover, the time-resolved KER spectra show characteristic fingerprints of quantum interference effects during the energy-transfer process. Our findings pave the way to elucidating quantum-interference effects in ultrafast charge- and energy-transfer dynamics in more complex systems, such as molecular clusters and solvated molecules.