The multiheterocyclic ring system shows valuable pharmaceutical and biological activities. In the present study, a microwave-assisted three-component reaction between aryl aldehyde, malononitrile, and 5-methyl-2,4-dihydro-3H-pyrazole-3-one led to the synthesis of pyrano[2,3-c]pyrazoles has been described. The reaction was carried out under solvent-free conditions in the presence of a new magnetically recoverable nanocatalyst (CoFe2O4@SiO2-HClO4). The reported protocol offers several advantages such as being environmentally benign, being rapid, inexpensive, having high atom and step economy, and being facile. The simple method of catalyst preparation, easy magnetic recovery, and reusability of the catalyst for four runs are notable features of the nanocatalyst. Antibacterial activity of all synthesized compounds was tested against Escherichia coli and Staphylococcus aureus. All synthesized compounds showed promising biological activity and may be used as a potential antibacterial candidate in biological science.