  In the light of the discovery of a 126 GeV Standard-Model-like Higgs boson at
the LHC, we evaluate the achievable accuracies for direct measurements of the
width, mass, and the s-channel resonant production cross section of the Higgs
boson at a proposed muon collider. We find that with a beam energy resolution
of R=0.01% (0.003%) and integrated luminosity of 0.5 fb^{-1} (1 fb^{-1}), a
muon collider would enable us to determine the Standard-Model-like Higgs width
to +/- 0.35 MeV (+/- 0.15 MeV) by combining two complementary channels of the
WW^* and b\bar b final states. A non-Standard-Model Higgs with a broader width
is also studied. The unparalleled accuracy potentially attainable at a muon
collider would test the Higgs interactions to a high precision.
