Background: Bacterial superinfections are common complications during viral infections, but the impact of multidrug-resistant (MDR) pathogens in critically ill patients affected by coronavirus disease 2019 (COVID-19) is still debated. Methods: This is an observational, monocentric, and prospective study designed to investigate the incidence, risk factors, and outcomes of MDR bacterial superinfections in COVID-19 patients admitted to the intensive care unit (ICU). Results: A high incidence of superinfections (66%, 159/241) was observed: ventilator-associated pneumonia (VAP) (65%, 104/159) and bloodstream infection (BSI, 32%, 51/159) were the most common. Superinfections, Extra-Corporeal Membrane Oxygenation (ECMO) support, and prone positioning increased the risk of death five, four, and more-than-two times, respectively (OR = 5.431, IC 95%: 1.637–18.014; 4.462, IC 95%: 1.616–12.324 and 2.346, IC 95%: 1.127–4.883). MDR bacteria were identified in 61% of patients with superinfection, with a cumulative incidence of 37.2% at day 14. Carbapenem-resistant Acinetobacter baumannii (CR-AB) and CR-Klebsiella pneumoniae (CR-KP) were the most common causative agents (24.3% and 13.7%). CR-AB was found to significantly increase both ICU and in-hospital mortality (76.4% and 78.2%), whereas CR-KP had no direct impact on mortality. Prior rectal colonization (p < 0.0001), mechanical ventilation (p = 0.0017), a prolonged ICU stay (p < 0.0001), the use of iNO (p = 0.0082), vasopressors (p = 0.0025), curarization (p = 0.0004), and prone positioning (p = 0.0084) were found to be risk factors for CR-AB. Conclusions: Critically ill COVID-19 patients are at high risk of developing MDR superinfection. While CR-KP had no direct impact on mortality, CR-AB appeared to increase ICU and in-hospital mortality.