  Recent developments of the nuclear emulsion technology led to the production
of films with nanometric silver halide grains suitable to track low energy
nuclear recoils with submicrometric length. This improvement opens the way to a
directional Dark Matter detection, thus providing an innovative and
complementary approach to the on-going WIMP searches. An important background
source for these searches is represented by neutron-induced nuclear recoils
that can mimic the WIMP signal. In this paper we provide an estimation of the
contribution to this background from the intrinsic radioactive contamination of
nuclear emulsions. We also report the induced background as a function of the
read-out threshold, by using a GEANT4 simulation of the nuclear emulsion,
showing that it amounts to about 0.06 neutrons per year per kilogram, fully
compatible with the design of a 10 kg$\times$year exposure.
