Chloroquine (CQ) and hydroxychloroquine (HCQ) have recently become the focus of global attention as possible treatments for Coronavirus Disease 2019 (COVID-19). The current systematic review aims to assess their safety in short treatments (≤14 days), whether used alone or in combination with other drugs. Following the PRISMA and SWiM recommendations, a search was conducted using four health databases for all relevant English-, Chinese-, and Spanish-language studies from inception through 30 July 2021. Patients treated for any condition and with any comparator were included. The outcomes of interest were early drug adverse effects and their frequency. A total of 254 articles met the inclusion criteria, including case and case-control reports as well as cross-sectional, cohort, and randomised studies. The results were summarised either qualitatively in table or narrative form or, when possible (99 studies), quantitatively in terms of adverse event frequencies. Quality evaluation was conducted using the CARE, STROBE, and JADAD tools. This systematic review showed that safety depended on drug indication. In COVID-19 patients, cardiac adverse effects, such as corrected QT interval prolongation, were relatively frequent (0–27.3% and up to 33% if combined with azithromycin), though the risk of torsade de pointes was low. Compared to non-COVID-19 patients, COVID-19 patients experienced a higher frequency of cardiac adverse effects regardless of the regimen used. Dermatological adverse effects affected 0–10% of patients with autoimmune diseases and COVID-19. A broad spectrum of neuropsychiatric adverse effects affected patients treated with CQ for malaria with variable frequencies and some cases were reported in COVID-19 patients. Gastrointestinal adverse effects occurred regardless of drug indication affecting 0–50% of patients. In conclusion, CQ and HCQ are two safe drugs widely used in the treatment of malaria and autoimmune diseases. However, recent findings on their cardiac and neuropsychiatric adverse effects should be considered if these drugs were to be proposed as antivirals again.