Background: Patients with rheumatoid arthritis (RA) have an increased risk of SARS-CoV-2 infection due to intrinsic characteristics of the pathology and the medications used to treat it. The aim was to evaluate the incidence of and factors related to SARS-CoV-2 infection in patients with RA in Colombia. Methods: This was an observational study of patients diagnosed with RA who were treated at a health care institution in Colombia. The study evaluated whether the patients presented SARS-CoV-2 infection and other clinical variables. Variables associated with the risk of SARS-CoV-2 infection were identified. Results: A total of 2566 patients with RA were identified. They had a median age of 61.9 years, and 81.1% were women. They were mainly treated with synthetic disease-modifying antirheumatic drugs (DMARDs) (85.3%), glucocorticoids (52.2%), and biological DMARDs (26.8%). The incidence of SARS-CoV-2 infection was 5.1%, and the factors that increased the risk included treatment with synthetic DMARDs with or without biological DMARDs but with concomitant systemic glucocorticoids [odds ratio (OR): 2.18, 95% confidence interval (CI): 1.21–3.93 and OR: 1.69, 95% CI: 1.05–2.74, respectively] and receiving antidiabetic drugs (OR: 2.24, 95% CI: 1.27–3.94). A total of 20.8% of patients with COVID-19 required hospitalization and 3.8% died. Conclusion: The incidence of COVID-19 is higher among patients with RA who receive DMARDs and glucocorticoids simultaneously or who have diabetes mellitus than among patients with RA not receiving these drug combinations, which should guide treatment strategies.