The fine structure of excited excitonic states in a quantum dot with an embedded magnetic ion is studied theoretically and experimentally. The developed theory takes into account the Coulomb interaction between charged carriers, the anisotropic long-range electron-hole exchange interaction in the zero-dimensional exciton, and the exchange interaction of the electron and the hole with the d electrons of a Mn ion inserted inside the dot. Depending on the relation between the quantum dot anisotropy and the exciton-Mn coupling, the photoluminescence excitation spectrum has a qualitatively different behavior. It provides a deep insight into the spin structure of the excited excitonic states.