Phytogenically synthesised nanoparticle (NP)-based drug delivery systems have promising potential in the field of biopharmaceuticals. From the point of view of biomedical applications, such systems offer the small size, high surface area, and possible synergistic effects of NPs with embedded biomolecules. This article describes the synthesis of silver nanoparticles (Ag-NPs) using extracts from the flowers and leaves of tansy (Tanacetum vulgare L.), which is known as a remedy for many health problems, including cancer. The reducing power of the extracts was confirmed by total phenolic and flavonoid content and antioxidant tests. The Ag-NPs were characterised by various analytical techniques including UV–vis spectroscopy, scanning electron microscopy (SEM), energy-dispersive spectrometry (EDS), Fourier transform infrared (FT-IR) spectroscopy, and a dynamic light scattering (DLS) system. The obtained Ag-NPs showed higher cytotoxic activity than the initial extracts against both human cervical cancer cell lines HeLa (ATCC CCL-2) and human melanoma cell lines A375 and SK-MEL-3 by MTT assay. However, the high toxicity to Vero cell culture (ATCC CCL-81) and human fibroblast cell line WS-1 rules out the possibility of their use as anticancer agents. The plant-mediated Ag-NPs were mostly bactericidal against tested strains with MBC/MIC index ≤4. Antifungal bioactivity (C. albicans, C. glabrata, and C. parapsilosis) was not observed for aqueous extracts (MIC > 8000 mg L−1), but Ag-NPs synthesised using both the flowers and leaves of tansy were very potent against Candida spp., with MIC 15.6 and 7.8 µg mL−1, respectively.