The problem of antibiotic resistance among pathogens encourages searching for novel active molecules. The aim of the research was to assay the anti-quorum sensing (anti-QS) and antibiofilm potential of Melaleuca alternifolia essential oil and its main constituent, terpinen-4-ol, to prevent the infections due to methicillin-resistant Staphylococcus aureus strains as an alternate to antibiotics. The tea tree oil (TTO) was evaluated for its potential in inhibiting QS-dependent phenomena such as violacein production in Chromobacterium violaceum, swarming motility of Pseudomonas aeruginosa PAO1, and biofilm formation in MRSA strains on glass. The results showed that terpinen-4-ol was able to inhibit MRSA strain biofilm formation on the glass strips by 73.70%. TTO inhibited the violacein production at a mean inhibitory concentration (MIC) value of 0.048 mg/mL by 69.3%. At 100 µg/mL TTO and terpinen-4-ol exhibited inhibition in swarming motility of PAO1 by 33.33% and 25%, respectively. TTO revealed anti-QS and anti-biofilm activities at very low concentrations, but it could be further investigated for new molecules useful for the treatment of MRSA infections.