  Extending the Minimal Supersymmetric Standard Model (MSSM) to explain small
neutrino masses via the inverse seesaw mechanism can lead to a new light
supersymmetric scalar partner which can play the role of inelastic dark matter
(iDM). It is a linear combination of the superpartners of the neutral fermions
in the theory (the light left-handed neutrino and two heavy Standard Model
singlet neutrinos) which can be very light with mass in $\sim 5-20$ GeV range,
as suggested by some current direct detection experiments. The iDM in this
class of models has keV-scale mass splitting, which is intimately connected to
the small Majorana masses of neutrinos. We predict the differential scattering
rate and annual modulation of the iDM signal which can be testable at future
Germanium- and Xenon-based detectors.
