Methicillin-resistant S. aureus (MRSA) are a threat to public health as they frequently reveal a multidrug-resistant pattern. Researchers all over the world are on an urgent hunt for new treatments to help fight infections before antibiotics become obsolete, and some natural alternatives, such as polyphenols, have already exhibited therapeutic properties. Therefore, this study aimed to determine the phenolic profile, antioxidant capacity, and antimicrobial activity against MRSA of the leaf, fruit, and stem bark extracts of Platanus hybrida. The polyphenols were extracted with a water/ethanol (20:80) mixture and the methodology included HPLC-DAD, DPPH, FRAP, and CuPRAC. To address this issue from a One Health perspective, the Kirby–Bauer disc diffusion method was performed against nine MRSA strains from three different sources (livestock, wild animals, and humans). Fourteen phenolics were identified and the leaf extract showed the highest phenolic content, followed by the fruit extract. The leaf extract also showed the highest antioxidant capacity while the fruit extract had the lowest antioxidant capacity. Both leaf and fruit extracts inhibited the growth of strains from all sources, while the stem bark extract did not inhibit the growth of human strains. This work highlights the complex chemical composition and the antioxidative and antimicrobial potential of extracts derived from P. hydrida.