  We study scalar Non-Standard Neutrino Interactions (NSI) induced by moduli or
flavon exchange between electrons and neutrinos. In a region with non-vanishing
electron number density, they are known to determine a shift of the neutrino
mass matrix. We review and extend the relevant formalism, and we update the
existing limits on electron and neutrino scalar couplings. We explore the
observability of scalar NSI in models of lepton masses based on flavour
symmetries. We analyze models where the scalar couplings are constrained either
by abelian symmetries or by modular invariance. We highlight regions of the
parameter space where observable effects can occur.
