The emergence of multidrug-resistant (MDR) bacteria has increased the need for alternative antimicrobial agents from natural sources. Propolis, a resinous bee product produced by honey bees (Apis mellifera) from plant resins, is rich in bioactive compounds with recognized antimicrobial and antioxidant properties. This study evaluated the phytochemical composition, antioxidant capacity, and antibacterial activity of propolis extracts obtained using ethanol, methanol, acetone, and water against clinically relevant MDR bacterial isolates. Total phenolic content was determined using the Folin–Ciocalteu assay, total flavonoid content by the aluminum chloride colorimetric method, and condensed tannin content by the butanol–HCl assay. Antioxidant activity was assessed using the 2,2′-azinobis-(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), 2,2-diphenyl-1-picrylhydrazyl (DPPH), and ferric reducing antioxidant power (FRAP) assays. Antibacterial activity was evaluated through minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC), MBC/MIC ratio, biofilm formation inhibition, and bacterial growth inhibition assays against MDR isolates of Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa, Enterococcus faecium, and Enterobacter cloacae. Significant differences among extraction solvents were observed for all phytochemical and antioxidant parameters (p < 0.0001). Ethanolic extracts exhibited the highest concentrations of total phenolics, flavonoids, and condensed tannins, as well as the greatest antioxidant activity. MIC values ranged from 3.13 to 25 mg/mL, whereas MBC values ranged from 6.25 to >50 mg/mL depending on bacterial species and extraction solvent. E. coli and E. faecium were the most susceptible isolates, while P. aeruginosa and E. cloacae showed greater tolerance. Most MBC/MIC ratios indicated bactericidal activity. Biofilm inhibition was significantly affected by bacterial strain and extraction solvent (p < 0.001), with ethanolic extracts producing the highest inhibition percentages. These findings demonstrate that ethanolic propolis extracts exhibit strong antioxidant activity, as well as bacteriostatic, bactericidal, and biofilm-formation-inhibitory effects, supporting their potential as complementary antimicrobial agents within a One Health framework.