Metal oxide nanoparticles have attained notable recognition due to their interesting physicochemical properties. Although these nanoparticles can be synthesized using a variety of approaches, the biological method involving plant extracts is preferred since it provides a simple, uncomplicated, ecologically friendly, efficient, rapid, and economical way for synthesis. In this study, the Azadirachta indica leaf extract was used as a reducing agent, and a green process was used to synthesize tin(ferrous: nickel)dioxide (Sn(Fe : Ni)O2) nanoparticles. The synthesized nanoparticles were subjected to characterization by using X-ray diffraction (XRD), energy-dispersive X-ray (EDX) spectroscopy analysis, field emission scanning electron microscopy (FESEM), Fourier transform infrared (FTIR) spectroscopy, dynamic light scattering (DLS), and photoluminescence (PL) measurement. Furthermore, Sn(Fe : Ni)O2 nanoparticles were analyzed for their antimicrobial activity against Gram-positive and Gram-negative organisms including Staphylococcus aureus, Streptococcus pneumoniae, Bacillus subtilis, Klebsiella pneumoniae, Escherichia coli, and Pseudomonas aeruginosa bacterial strains. XRD patterns revealed that Sn(Fe : Ni)O2 nanoparticles exhibited a tetragonal structure. The hydrodynamic diameter of the nanoparticles was 143 nm, as confirmed by the DLS spectrum. The FESEM image showed the spherical form of the synthesized nanoparticles. Chemical composites and mapping analyses were performed through the EDAX spectrum. The Sn–O–Sn and Sn–O stretching bands were 615 cm−1 and 550 cm−1 in the FTIR spectrum, respectively. Various surface defects of the synthesized Sn(Fe : Ni)O2 nanoparticles were identified by photoluminescence spectra. Compared to traditional antibiotics like amoxicillin, the inhibition zone revealed that Sn(Fe : Ni)O2 nanoparticles displayed remarkable antibacterial activity against all tested organisms, indicating the valuable potential of nanoparticles in the healthcare industry.