Liver cancer is the leading cause of cancer‑related mortality worldwide and its incidence is increasing. Considerable effort has been made in recent decades to improve the diagnosis and treatment of liver cancer. Advanced liver cancer often exhibits a poor response to chemotherapy and poor prognosis due to acquired chemoresistance and tumor recurrence. Understanding the precise molecular mechanisms that are responsible for chemotherapeutic drug‑induced cell death could potentially identify novel therapeutic targets and improve liver cancer treatment. In the present study, it was demonstrated that in response to doxorubicin, the most frequently used chemical compound for liver cancer treatment, histone deacetylase sirtuin 6 (SIRT6) is specifically downregulated. This enables forkhead box O3 (FOXO3) upregulation, translocation into the nucleus and increased expression of its target genes p27 and Bim, which further induce apoptosis. Overexpression of SIRT6, but not enzyme‑inactivated mutants, prevents FOXO3 translocation into the nucleus and doxorubicin‑induced cell death. SIRT6 interacts with FOXO3 and this interaction increases FOXO3 ubiquitination and decreases its stability. Finally, it was identified that the effect of SIRT6 in preventing doxorubicin‑induced cell death requires FOXO3. Overexpression of SIRT6 could not prevent doxorubicin‑induced cell death in FOXO3‑knockdown cells. Therefore, it was concluded that SIRT6 plays a central role in determining doxorubicin‑induced cell death via modulation of FOXO3 activity. Therapeutic targeting of SIRT6 and/or FOXO3 may offer novel strategies for treatment of liver cancer.