Andrographolide, a medicinal compound, exhibits several pharmacological activities, including antiviral and anticancer properties. Previously, we reported that andrographolide inhibits Epstein–Barr virus (EBV) lytic reactivation, which is associated with viral transmission and oncogenesis in epithelial cancers, including head-and-neck cancer (HNC) cells. However, the underlying mechanism through which andrographolide inhibits EBV lytic reactivation and affects HNC cells is poorly understood. Therefore, we investigated these mechanisms using EBV-positive HNC cells and the molecular modeling and docking simulation of protein. Based on the results, the expression of EBV lytic genes and viral production were significantly inhibited in andrographolide-treated EBV-positive HNC cells. Concurrently, there was a reduction in transcription factors (TFs), myocyte enhancer factor-2D (MEF2D), specificity protein (SP) 1, and SP3, which was significantly associated with a combination of andrographolide and sodium butyrate (NaB) treatment. Surprisingly, andrographolide treatment also significantly induced the expression of DNA Methyltransferase (DNMT) 1, DNMT3B, and histone deacetylase (HDAC) 5 in EBV-positive cells. Molecular modeling and docking simulation suggested that HDAC5 could directly interact with MEF2D, SP1, and SP3. In our in vitro study, andrographolide exhibited a stronger cytotoxic effect on EBV-positive cells than EBV-negative cells by inducing cell death. Interestingly, the proteome analysis revealed that the expression of RIPK1, RIPK3, and MLKL, the key molecules for necroptosis, was significantly greater in andrographolide-treated cells. Taken together, it seems that andrographolide exhibits concurrent activities in HNC cells; it inhibits EBV lytic reactivation by interrupting the expression of TFs and induces cell death, probably via necroptosis.