(1) Background: The aim of this study was to assess the effects of the COVID-19 pandemic on the use and outcomes of cardiac procedures among people with chronic obstructive pulmonary disease (COPD) in Spain. (2) Methods: We used national hospital discharge data to select patients admitted to hospital with a diagnosis of COPD from 1 January 2019 to 31 December 2020. (3) Results: The number of COPD patients hospitalized in 2019 who underwent a cardiac procedure was 4483, 16.2% higher than in 2020 (n = 3757). The length of hospital stay was significantly lower in 2020 than in 2019 (9.37 vs. 10.13 days; p = 0.004), and crude in-hospital mortality (IHM) was significantly higher (5.32% vs. 4.33%; p = 0.035). Multivariable logistic regression models to assess the differences in IHM from 2019 to 2020 showed Odds Ratio (OR) values over 1, suggesting a higher risk of dying in 2020 compared to in 2019. However, the ORs were only statistically significant for “any cardiac procedure” (1.18, 95% CI 1.03–1.47). The Charlson comorbidity index increased IHM for each of the procedures analyzed. The probability of IHM was higher for women and older patients who underwent coronary artery bypass graft or open valve replacement procedures. Suffering a COVID-19 infection was associated with significantly higher mortality after cardiac procedures. (4) Conclusions: The COVID-19 pandemic limited the access to healthcare for patients with COPD.