Implication on Higgs invisible width in light of the new CDMS result

With the assumption that the dominant diagram in supersymmetry for the spin-independent cross section of the dark matter particle is due to Higgs boson exchange, we obtain an upper limit on the Higgs-dark-matter coupling based on the new result of the CDMSII Collaborations. We then obtain an upper limit on the invisible width of the Higgs boson, numerically it is less than 20-120 MeV for $m_h \simeq 120 - 180$ GeV. Implications for Higgs boson search are also discussed.