  The ATLAS and CMS collaborations have recently reported tantalizing hints of
the existence of a 125 GeV Higgs--like particle, whose couplings appear to
match well the Standard Model (SM) expectations. In this work, we study
implications of this observation for the neutralino sector of supersymmetric
models, assuming that the Higgs signal gets confirmed. In general, the Higgs
decay into neutralinos can be one of its dominant decay channels. Since a large
invisible Higgs decay branching ratio would be in conflict with the data, this
possibility is now constrained. In particular, we find that most of the region
mu < 170 GeV, M_1 < 70 GeV at tan beta ~ 10 and mu < 120 GeV, M_1 < 70 GeV at
tan beta ~ 40 is disfavored.
