  We show that a minimal local $B-L$ symmetry extension of the standard model
can provide a unified description of both neutrino mass and dark matter. In our
model, $B-L$ breaking is responsible for neutrino masses via the seesaw
mechanism, whereas the real part of the $B-L$ breaking Higgs field (called
$\sigma$ here) plays the role of a freeze-in dark matter candidate for a wide
parameter range. Since the $\sigma$-particle is unstable, for it to qualify as
dark matter, its lifetime must be longer than $10^{25}$ seconds implying that
the $B-L$ gauge coupling must be very small. This in turn implies that the dark
matter relic density must arise from the freeze-in mechanism. The dark matter
lifetime bound combined with dark matter relic density gives a lower bound on
the $B-L$ gauge boson mass in terms of the dark matter mass. We point out
parameter domains where the dark matter mass can be both in the keV to MeV
range as well as in the PeV range. We discuss ways to test some parameter
ranges of this scenario in collider experiments. Finally, we show that if
instead of $B-L$, we consider the extra $U(1)$ generator to be
$-4I_{3R}+3(B-L)$, the basic phenomenology remains unaltered and for certain
gauge coupling ranges, the model can be embedded into a five dimensional
$SO(10)$ grand unified theory.
