Pseudomonas aeruginosa is a commonly found Gram-negative bacterium in healthcare facilities and is renowned for its ability to form biofilms and its virulence factors that are controlled by quorum sensing (QS) systems. The increasing prevalence of multidrug-resistant strains of this bacterium poses a significant challenge in the field of medicine. Consequently, the exploration of novel antimicrobial agents has become a top priority. This research aims to optimize chitosan derived from white shrimp (Metapenaeus affinis) using the Response Surface Methodology (RSM) computational approach. The objective is to investigate chitosan’s potential as a solution for inhibiting QS activity and biofilm formation in P. aeruginosa ATCC 10,145. Under optimized conditions, chitin was treated with NaOH (1.41 M) for 15.75 h, HCl (7.49% vol) for 2.01 h, and at a deacetylation temperature of 81.15 °C. The resulting chitosan exhibited a degree of deacetylation (DD%) exceeding 93.98%, as confirmed by Fourier-transform infrared (FTIR) spectral analysis, indicating its high purity. The extracted chitosan demonstrated a significant synergistic antibiotic effect against P. aeruginosa when combined with ceftazidime, enhancing its bactericidal activity by up to 15-fold. In addition, sub-MIC (minimum inhibitory concentration) concentrations of extracted chitosan (10 and 100 µg/mL) successfully reduced the production of pyocyanin and rhamnolipid, as well as the swimming motility, protease activity and biofilm formation ability in comparison to the control group (P < 0.05). Moreover, chitosan treatment downregulated the RhlR and LasR genes in P. aeruginosa when compared to the control group (P < 0.05). The optimized chitosan extract shows significant potential as a coating agent for surgical equipment, effectively preventing nosocomial infections caused by P. aeruginosa pathogens.