Muon $g-2$ at multi-TeV muon collider

The long-standing discrepancy of muon $g-2$ is a hint of new physics beyond the standard model of particle physics. In this letter we show that heavy new physics contribution can be fully tested at a muon collider with center-of-mass energy up to $O(10)\,$TeV. Even if there is no new particle in this energy range, one can measure the $g-2$ directly via the channel to a Higgs boson and a monochromatic photon.