Summary: The anomalous \(ZZ\gamma\) and \(Z\gamma\gamma\) neutral triple gauge couplings occurred by dimension-eight operators are investigated through the process \(\mu^+\mu^-\to\mu^+\gamma^\ast\mu^-\to\mu^+ Z(\nu\bar{\nu})\mu^-\) at the muon collider with \(\sqrt{s} = 3\), 6, 10 and 14 TeV. The charged lepton pseudo-rapidity, the charged lepton transverse momentum and the transverse missing energy distributions are taken in consideration for the final state of the process in the analysis. The sensitivities of the anomalous couplings are obtained at 95% Confidence Level with integrated luminosity of \(\mathcal{L}_{\mathrm{int}} = 1\), 4, 10 and \(20\,\mathrm{ab}^{-1}\), respectively, according to center-of-mass energies of muon collider taking into account the effects of systematic uncertainties 0%, 3% and 5%. The best limits of anomalous \(C_{BB}/\Lambda^4\), \(C_{B W}/\Lambda^4\), \(C_{\widetilde{B}W}/\Lambda^4\) and \(C_{WW}/\Lambda^4\) couplings without systematic uncertainty at center-of-mass energy of 14 TeV and integrated luminosity of \(20\,\mathrm{ab}^{-1}\) are found to be \([-0.01026; 0.00636]\,\mathrm{TeV}^{-4}\), \([-0.02482; 0.03053]\,\mathrm{TeV}^{-4}\), \([-0.01830; 0.02510]\,\mathrm{TeV}^{-4}\), \([-0.06981; 0.07387]\,\mathrm{TeV}^{-4}\), respectively.