Novel and powerful fibroin‐functionalized magnetic carbon nanotube–supported silver nanoparticles (CNT–Fe3O4–fibroin–Ag) were successfully synthesized as a nontoxic and inexpensive biocatalyst. The structure of the organic–inorganic hybrid bionanocomposite was characterized by various techniques such as Fourier transform infrared spectroscopy, thermogravimetric analysis, energy‐dispersive X‐ray, field emission‐scanning electron microscopy, transmission electron microscopy, X‐ray diffraction, vibrating sample magnetometry, atomic absorption spectroscopy, and inductively coupled plasma‐optical emission spectrometry. Then, the catalytic activity of synthesized bionanocomposite was evaluated in the three‐component A3 coupling reaction under solvent‐free conditions with good to excellent yields. Several propargylamine derivatives were synthesized by the reaction of different aldehydes with amines and phenylacetylene. Biodegradability, biocompatibility, availability, easy synthesis, high stability, high‐throughput, cost‐effectiveness, and efficient magnetic separation are some advantages of this catalyst that make it economically justified and sustainable. Moreover, the catalyst can be recycled for several runs without appreciable loss in its catalytic activity.