(1) Background: The aim of this study was to assess the incidence and the risk factors for healthcare-associated Clostridioides difficile infection (HA-CDI) in patients with COVID-19 and without this infection. (2) Methods: A single-center, prospective observational study was conducted at the University Clinical Hospital Center in Belgrade, Serbia, from January 2019 to December 2021. The entire hospital was a COVID-dedicated hospital for 12 months during the study period. The incidence density rates and risk factors for HA-CDI in patients with and without COVID-19 are presented. (3) Results: The incidence rates of HA-CDIs were three times higher in patients with COVID-19. The HA-CDI–COVID-patients were younger (69.9 ± 12.6 vs. 72.5 ± 11.6; p = 0.017), admitted from another hospital (20.5% vs. 2.9; p < 0.001), had antimicrobial therapy before CDI (99.1% vs. 91.3%, p < 0.001), received two or more antibiotics (p = 0.030) during a longer period (p = 0.035), received proton pump inhibitors (95.9% vs. 50.0%, p < 0.001) during a longer period (p = 0.012) and steroids (32.8% vs. 20.4%, p < 0.001). During the last month before their current hospitalization, a higher percentage of patients without COVID-19 disease were hospitalized in our hospital (p < 0.001). Independent predictors for HA-CDIs in patients with COVID-19 were admission from another hospital (p = 0.003), the length of antibiotic administration (0.020), and the use of steroids in therapy (p < 0.001). The HA-CDI predictors in the non-COVID patients were older age (p = 0.017), advanced-stage renal failure (p = 0.005), chemotherapy (p = 0.003), and a low albumin level (0.005). (4) Conclusion: Higher incidence rates of HAI-CDIs in COVID-19 patients did not occur due to reduced infection control precautions and hygiene measures but due to antibiotic therapy and therapy with other drugs used during the pandemic.