We study the excited muon production at the FCC-based muon-hadron colliders. We give the excited muon decay widths and production cross-sections. We deal with the µp → µ ⋆ q → µγq process and we plot the transverse momentum and normalized pseudorapidity distributions of final state particles to define the kinematical cuts best suited for discovery. By using these cuts, we get the mass limits for excited muons. It is shown that the discovery limits obtained on the mass of µ ⋆ are 2.2, 5.8, and 7.5 TeV for muon energies of 63, 750, and 1500 GeV, respectively.