Within the framework of a constrained Minimal Supersymmetric Standard Model (cMSSM) augmented by an MSSM singlet-pair sector to account for the non-zero neutrino masses by inverse seesaw mechanism, the lightest supersymmetric particle (LSP) can be a mixed sneutrino with mass as small as 50 GeV, satisfying all existing constraints, thus qualifying as a light dark matter candidate. We study the possibility of the lightest neutral Higgs boson in this model decaying invisibly into a pair of sneutrino LSPs, thereby giving rise to novel missing energy signatures at the LHC. We perform a two-parameter global analysis of the LHC Higgs data available till date to determine the optimal invisible Higgs branching fraction in this scenario, and obtain a $2σ(1σ)$ upper limit of 0.23 (0.12). A detailed cut-based analysis is carried out thereafter, demonstrating the viability of our proposed signal vis-a-vis backgrounds at the LHC. ; Comment: 29 pages, 10 figures and 7 tables. Text and references added, some numbers changed slightly due to a small error in coding. To appear in JHEP