In the present work, a novel heterogeneous catalytic system involving copper(I) complex of moisture- and air-stable organoselenium ligand supported on Fe3O4 nanoparticles modified by SiO2/aminopropyltrieethoxysilane was designed, synthesized, and characterized using various physicochemical methods inclusive Fourier transform infrared spectroscopy, X-ray diffraction, vibrating sample magnetometry, field emission scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, atomic absorption spectroscopy, inductively coupled plasma optical emission spectroscopy, and thermogravimetry. The catalytic activity of the synthesized magnetic nanocatalyst which was named Fe3O4@SiO2-Se-T/CuI was evaluated in A(3) coupling reactions for the preparation of propargylamine compounds using diverse aldehydes, secondary amines, and terminal alkynes. The benign reaction condition, variety of substrate scope, good yield, low reaction time, high stability, utilization of organoselenium compound as an air- and moisture-insensitive ligand and its immobilization on solid support, and, more importantly, effortless recovery and recyclability of the catalyst up to five consecutive cycles without remarkable loss in its activity are some of the interesting features of this protocol that makes it more beneficial from both industrial and environmental points of view.