For the Mott insulator state of the Fermi-Hubbard model in the strong-coupling limit, we study the interaction between quasi-particles in the form of doublons and holons. Comparing different methods – the hierarchy of correlations, strong-coupling perturbation theory, and exact analytic solutions for the Hubbard tetramer – we find an effective interaction between doublons and/or holons to linear order in the hopping strength which can display attractive as well as repulsive contributions, depending on the involved momenta. Finally, we speculate about the implications of our findings for high-temperature superconductivity.