A new mechanism for generating neutrino masses without a high-energy mass scale is proposed. The mechanism needs a fundamental mass scale M in the 100--1000 TeV region and a minimal field content beyond the Standard Model one containing a pair of fermion singlets and a pair of weak doublet fermions for each neutrino mass, all of them with a mass of order M. The neutrino mass appears by a multiple seesaw-type tree-level diagram. We provide an explicit model based on supersymmetry and an Abelian symmetry which provides the required fermion mass matrix. The mechanism is natural in the context of string theories with a low fundamental scale. Within an explicit example where the Abelian symmetry is also responsible for the generation of fermion masses and mixings, we give a hint relating the fermion mass matrices and the weak mixing angle. By assuming the weak--strong couplings unification, one naturally finds \sin² \theta _w = 1/4 at the fundamental scale.

PACS numbers: 14.60.Pq, 14.60.St, 12.60.Jv