Since summer 2020, SARS-CoV-2 strains at the origin of the COVID-19 pandemic have suddenly been replaced by new SARS-CoV-2 variants, some of which are highly transmissible and spread at a high rate. These variants include the Marseille-4 lineage (Nextclade 20A.EU2) in Europe, the 20I/501Y.V1 variant first detected in the UK, the 20H/501Y.V2 variant first detected in South Africa, and the 20J/501Y.V3 variant first detected in Brazil. These variants are characterized by multiple mutations in the viral spike protein that is targeted by neutralizing antibodies elicited in response to infection or vaccine immunization. The usual coronavirus mutation rate through genetic drift alone cannot account for such rapid changes. Recent reports of the occurrence of such mutations in immunocompromised patients who received remdesivir and/or convalescent plasma or monoclonal antibodies to treat prolonged SARS-CoV-2 infections led us to hypothesize that experimental therapies that fail to cure the patients from COVID-19 could favor the emergence of immune escape SARS-CoV-2 variants. We review here the data that support this hypothesis and urge physicians and clinical trial promoters to systematically monitor viral mutations by whole-genome sequencing for patients who are administered these treatments.