  We develop a systematic theory for excitons subject to Fermi-Hubbard physics
in moir\'e twisted transition metal dichalcogenides (TMDs). Specifically, we
consider excitons in moir\'e systems for which the valence band is in the
Mott-insulating regime. These "Mott-moir\'e excitons", which are achievable in
twisted TMD heterobilayers, are bound states of a magnetic polaron in the
valence band and a free electron in the conduction band. We find significantly
narrower exciton bandwidths in the presence of Hubbard physics, serving as a
potential experimental signature of strong correlations. We also demonstrate
the high tunability of Mott-moir\'e excitons through the dependence of their
binding energies, diameters, and bandwidths on the moir\'e period. Our work
provides guidelines for future exploration of strongly correlated excitons in
twisted TMD heterobilayers.
