The COVID-19 pandemic has strained healthcare systems globally. Shortages of hospital beds, reassignment of healthcare workers to COVID-19-dedicated wards, an increased workload, and evolving infection prevention and control measures have potentially contributed to the spread of multidrug-resistant bacteria (MDRB). To determine the impact of the COVID-19 pandemic at the University Medical Center Ljubljana, a tertiary teaching hospital, we analyzed the monthly incidence of select bacterial species per patient from 2018 to 2022. The analysis was performed for all isolates and for MDRB isolates. The data were analyzed separately for isolates from all clinical samples, from blood culture only, and from clinical and surveillance samples. Our findings revealed an increased incidence density of patients with Enterococcus faecium, Staphylococcus aureus, Escherichia coli, and Pseudomonas aeruginosa isolates from clinical samples during the COVID-19 period in the studied hospital. Notably, the incidence density of MDRB isolates—vancomycin-resistant E. faecium, extended-spectrum betalactamase-producing K. pneumoniae, and betalactam-resistant P. aeruginosa—from clinical samples increased during the COVID-19 period. There were no statistically significant differences in the incidence density of patients with blood culture MDRB isolates. We observed an increase in the overall MDRB burden (patients with MDRB isolates from both clinical and surveillance samples per 1000 patient days) in the COVID-19 period in the studied hospital for vancomycin-resistant E. faecium, carbapenem-resistant K. pneumoniae, and betalactam-resistant P. aeruginosa and a decrease in the methicillin-resistant S. aureus burden.