Along with genetic mutations, aberrant epigenetic alterations are the initiators of head and neck cancer carcinogenesis. Currently, several drugs are being developed to correct these epigenetic alterations, known as epidrugs. Some compounds with an antioxidant effect have been shown to be effective in preventing these malignant lesions and in minimizing the complications derived from cytotoxic treatment. Furthermore, in vitro and in vivo studies show a promising role in the treatment of head and neck squamous cell carcinoma (HNSCC). This is the case of supplements with DNA methylation inhibitory function (DNMTi), such as epigallocatechin gallate, sulforaphane, and folic acid; histone deacetylase inhibitors (HDACi), such as sodium butyrate and melatonin or histone acetyltransferase inhibitors (HATi), such as curcumin. The objective of this review is to describe the role of some antioxidants and their epigenetic mechanism of action, with special emphasis on melatonin and butyric acid given their organic production, in the prevention and treatment of HNSCC.