  We investigate the potential of a muon collider for testing the presence of
anomalous Higgs boson couplings. We consider the case of a light (less than
$160 GeV$) Higgs boson and study the effects on the Higgs branching ratios and
total width, which could be induced by the non standard couplings created by a
class of dim=6 $SU(3)\times SU(2)\times U(1)$ gauge invariant operators
satisfying the constraints imposed by the present and future hadronic and
$e^-e^+$ colliders. For each operator we give the minimal value of the
$\mu^+\mu^-$ integrated luminosity needed for the muon collider ($\mu C$) to
improve these constraints. Depending on the operator and the Higgs mass, this
minimal $\mu C$ luminosity lies between $0.1 fb^{-1}$ and $100 fb^{-1}$.
