During the COVID-19 pandemic, the implementation of antimicrobial stewardship strategies has been recommended. This study aimed to assess the impact of the COVID-19 pandemic in a tertiary care Spanish hospital with an active ongoing antimicrobial stewardship programme (ASP). For a 20-week period, we weekly assessed antimicrobial consumption, incidence density, and crude death rate per 1000 occupied bed days of candidemia and multidrug-resistant (MDR) bacterial bloodstream infections (BSI). We conducted a segmented regression analysis of time series. Antimicrobial consumption increased +3.5% per week (p = 0.016) for six weeks after the national lockdown, followed by a sustained weekly reduction of −6.4% (p = 0.001). The global trend for the whole period was stable. The frequency of empirical treatment of patients with COVID-19 was 33.7%. No change in the global trend of incidence of hospital-acquired candidemia and MDR bacterial BSI was observed (+0.5% weekly; p = 0.816), nor differences in 14 and 30-day crude death rates (p = 0.653 and p = 0.732, respectively). Our work provides quantitative data about the pandemic effect on antimicrobial consumption and clinical outcomes in a centre with an active ongoing institutional and education-based ASP. However, assessing the long-term impact of the COVID-19 pandemic on antimicrobial resistance is required.