We have studied anomalous four-photon couplings in the ${\mu }^{+}{\mu }^{-}\to {\mu }^{+}\gamma \gamma {\mu }^{-}$ scattering at a future muon collider. The collision energies of 3 TeV, 14 TeV, and 100 TeV are addressed. Both differential and total cross sections versus invariant mass of the outgoing photons are calculated. The best 95% C.L. exclusion bounds on anomalous couplings are obtained to be $g_1=2.23\times {10}^{-8}$ TeV$^{−4}$ and $g_2=4.22\times {10}^{-8}$ TeV$^{−4}$. They correspond to the muon collision energy of 100 TeV. The partial-wave unitary constraints on $g_1$ and $g_2$ are examined. We have demonstrated that the unitarity is not violated in a region of the anomalous couplings obtained in the present paper.