(1) Background and Objectives: The COVID-19 pandemic influenced the management of patients with immune-mediated rheumatic and musculoskeletal diseases (imRMDs) in various ways. The goal of our systematic review was to determine the influence of the first period of the COVID-19 pandemic (February 2020 to July 2020) on the management of imRMDs regarding the availability of drugs, adherence to therapy and therapy changes and on healthcare delivery. (2) Materials and Methods: We conducted a systematic literature search of PubMed, Cochrane and Embase databases (carried out 20–26 October 2021), including studies with adult patients, on the influence of the COVID-19 pandemic on the management of imRMDs. There were no restrictions regarding to study design except for systematic reviews and case reports that were excluded as well as articles on the disease outcomes in case of SARS-CoV-2 infection. Two reviewers screened the studies for inclusion, and in case of disagreement, a consensus was reached after discussion. (3) Results: A total of 5969 potentially relevant studies were found, and after title, abstract and full-text screening, 34 studies were included with data from 182,746 patients and 2018 rheumatologists. The non-availability of drugs (the impossibility or increased difficulty to obtain a drug), e.g., hydroxychloroquine and tocilizumab, was frequent (in 16–69% of patients). Further, medication non-adherence was reported among patients with different imRMDs and between different drugs in 4–46% of patients. Changes to preexisting medication were reported in up to 33% of patients (e.g., reducing the dose of steroids or the cessation of biological disease-modifying anti-rheumatic drugs). Physical in-office consultations and laboratory testing decreased, and therefore, newly implemented remote consultations (particularly telemedicine) increased greatly, with an increase of up to 80%. (4) Conclusions: The COVID-19 pandemic influenced the management of imRMDs, especially at the beginning. The influences were wide-ranging, affecting the availability of pharmacies, adherence to medication or medication changes, avoidance of doctor visits and laboratory testing. Remote and telehealth consultations were newly implemented. These new forms of healthcare delivery should be spread and implemented worldwide to routine clinical practice to be ready for future pandemics. Every healthcare service provider treating patients with imRMDs should check with his IT provider how these new forms of visits can be used and how they are offered in daily clinical practice. Therefore, this is not only a digitalization topic but also an organization theme for hospitals or outpatient clinics.