  The problem of Majorana neutrino mass generated in
Arkani-Hamed--Dimopoulos-Dvali model with n extra spatial dimensions is
discussed. Taking into account constraints on neutrino masses coming from
cosmological observations, it is possible to obtain lower limits on the size of
extra dimensions as large as 10^{-6} mm. In the case of n=4 it is easy to lower
the fundamental scale of gravity from the Planck energy to electroweak scale
\~TeV without imposing any additional constraints. A link between the half-life
of neutrinoless double beta decay and the size of extra dimensions is
discussed.
