While the relative efficacy of remdesivir as a therapeutic agent in selected patients with COVID-19 has been established, safety concerns have been raised regarding potential nephrotoxicity and hepatotoxicity. Our main objective was to investigate the kidney- and liver-related safety outcomes in patients with COVID-19 treated with remdesivir in a public hospital in New York. A propensity score-matched retrospective study was conducted in hospitalized patients with COVID-19 from 1 June 2020 to 10 March 2021. A total of 927 patients were included in this study (remdesivir: 427, non-remdesivir: 500; women: 51.8%; median age 61 years; median BMI: 28.5 kg/m²). Matching without replacement yielded a cohort of 248 patients (124 in each group). In the matched cohort, the remdesivir group had a significantly lower rate of acute kidney injury (AKI) (12.1% vs. 21.8%, p = 0.042), a lower rate of acute liver injury (ALI) on the verge of statistical significance (7.3% vs. 14.5%, p = 0.067), and non-significantly lower death rate (13.7% vs. 16.1%, p = 0.593) compared to the non-remdesivir group. Multivariable analyses revealed that patients treated with remdesivir were found to be associated with a significantly lower likelihood for AKI (OR: 0.40; 95% CI: 0.24–0.67, p < 0.001), no association was found for ALI (OR: 0.68; 95% CI: 0.35–1.30, p = 0.241), while a trend towards an association of patients treated with remdesivir with a lower likelihood for in-hospital death was observed (OR: 0.57; 95% CI: 0.32–1.01, p = 0.053). In conclusion, no safety concerns with regards to renal and liver outcomes were raised in patients with COVID-19 treated with remdesivir. Instead, there were signals of possible nephroprotection and improved in-hospital mortality.