Nanomaterial technology has attracted much attention because of its antibacterial and drug delivery properties, among other applications. Metal-organic frameworks (MOFs) have advantages, such as their pore structure, large specific surface area, open metal sites, and chemical stability, over other nanomaterials, enabling better drug encapsulation and adsorption. In two examples, we used the common pathogenic bacterium Staphylococcus aureus and highly infectious influenza A virus. A novel complex MIL-101(Fe)-T705 was formed by synthesizing MOF material MIL-101(Fe) with the drug favipiravir (T-705), and a hot solvent synthesis method was applied to investigate the in vitro antibacterial and antiviral activities. The results showed that MIL-101(Fe)-T705 combined the advantages of nanomaterials and drugs and could inhibit the growth of Staphylococcus aureus at a concentration of 0.0032 g/mL. Regarding the inhibition of influenza A virus, MIL-101(Fe)-T705 showed good biosafety at 12, 24, 48, and 72 h in addition to a good antiviral effect at concentrations of 0.1, 0.2, 0.4, 0.8, 1.6, and 3 μg/mL, which were higher than MIL-101(Fe) and T-705.