Fanconi anemia rare disease is characterized by bone marrow failure and a high predisposition to solid tumors, especially head and neck squamous cell carcinoma (HNSCC). Patients with Fanconi anemia with HNSCC are not eligible for conventional therapies due to high toxicity in healthy cells, predominantly hematotoxicity, and the only treatment currently available is surgical resection. In this work, we searched and validated two already approved drugs as new potential therapies for HNSCC in patients with Fanconi anemia. We conducted a high-content screening of 3,802 drugs in a FANCA-deficient tumor cell line to identify nongenotoxic drugs with cytotoxic/cytostatic activity. The best candidates were further studied in vitro and in vivo for efficacy and safety. Several FDA/European Medicines Agency (EMA)-approved anticancer drugs showed cancer-specific lethality or cell growth inhibition in Fanconi anemia HNSCC cell lines. The two best candidates, gefitinib and afatinib, EGFR inhibitors approved for non-small cell lung cancer (NSCLC), displayed nontumor/tumor IC50 ratios of approximately 400 and approximately 100 times, respectively. Neither gefitinib nor afatinib activated the Fanconi anemia signaling pathway or induced chromosomal fragility in Fanconi anemia cell lines. Importantly, both drugs inhibited tumor growth in xenograft experiments in immunodeficient mice using two Fanconi anemia patient-derived HNSCCs. Finally, in vivo toxicity studies in Fanca-deficient mice showed that administration of gefitinib or afatinib was well-tolerated, displayed manageable side effects, no toxicity to bone marrow progenitors, and did not alter any hematologic parameters. Our data present a complete preclinical analysis and promising therapeutic line of the first FDA/EMA-approved anticancer drugs exerting cancer-specific toxicity for HNSCC in patients with Fanconi anemia.