High rates of resistance to antibiotics are associated with healthcare-related infections, thus demonstrating the urgent need for effective antimicrobials against these maladies. The present study aims to determine the chemical composition of essential oil (EO) from Clausena anisata leaves and evaluate their antibacterial activity against selected nosocomial bacteria. To this end, one kilogram (1 kg) of fresh leaves of C. anisata was washed and boiled with 500 mL of distilled water for 2−4 h using a Clevenger apparatus. The oil was then collected in an Erlenmeyer, dried using anhydrous sodium sulfate, bottled in a tinted glass bottle and refrigerated at 4 °C before analysis. Next, the as-prepared oil was analyzed using gas chromatography-mass spectrometry (GC-MS). The essential oil was further tested against a panel of selected nosocomial bacteria, including Staphylococcus and Klebsiella species, among others, by microdilution using a resazurin assay to determine the minimum inhibitory and minimum bactericidal concentrations (MICs and MBCs, respectively). As a result, 0.77% of EO was extracted from fresh leaves of C. anisata. The GC-MS analysis revealed that the as-prepared essential oil contained E-anethole (70.77%), methyl isoeugenol (13.85%), estragole (4.10%), γ-terpinene (3.33%), myrcene (2.82%) and sabinene (0.77%), with E-anethole being the major constituent. Twenty-two compounds were identified in the EO of C. anisata leaves through gas chromatography. Upon antibacterial testing against selected nosocomial pathogens, the E-anethole-rich essential oil exhibited MIC and MBC values ranging from 3.91 to 125 µg/mL and 7.81 to 125 µg/mL, respectively, indicative of a bactericidal orientation of the plant’s essential oil (MIC/MBC ratio < 4). This novel contribution highlights the scientific validation of the use of C. anisata leaves in the traditional treatment of various infectious diseases. However, toxicity and pharmacokinetic studies, mechanistic bases of the antibacterial action, and in vivo antibacterial experiments of the E-anethole-rich EO of C. anisata should be investigated to successfully use this plant in the treatment of infectious diseases.