The unusual class of magnetized nonthermal radio filaments (NTF), threads and streaks with their unique physical characteristics are found only within the inner couple of degrees of the Galactic center. Also, a number of young, mass-losing and rare stellar clusters are recognized to lie in the Galactic center region. The latter characteristic of the Galactic center region is used to explain the origin of the nonthermal radio filaments. We consider a mechanism in which the collective winds of massive WR and OB stars within a dense stellar environment produce shock waves that can accelerate particles to relativistic energies. This mechanism is an extension of a model originally proposed by Rosner and Bodo (1996), who suggested that energetic nonthermal particles are produced in a terminal shock of mass-losing stars. The large-scale distribution of the magnetic field in the context of this model is argued to have neither poloidal geometry nor pervasive throughout the Galactic center region.