  We explore the sensitivity of directly testing the muon-Higgs coupling at a
high-energy muon collider. This is strongly motivated if there exists new
physics that is not aligned with the Standard Model Yukawa interactions which
are responsible for the fermion mass generation. We illustrate a few such
examples for physics beyond the Standard Model. With the accidentally small
value of the muon Yukawa coupling and its subtle role in the high-energy
production of multiple (vector and Higgs) bosons, we show that it is possible
to measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeV
muon collider and a few percent for a 30 TeV machine by utilizing the three
boson production, potentially sensitive to a new physics scale about $\Lambda
\sim 30-100$ TeV.
