The transcription factor p53 (also known as TP53) guards against tumour and virus replication and is inactivated in almost all cancers. p53-activated transcription of target genes is thought to be synonymous with the stabilization of p53 in response to oncogenes and DNA damage. During adenovirus replication, the degradation of p53 by E1B-55k is considered essential for p53 inactivation, and is the basis for p53-selective viral cancer therapies. Here we reveal a dominant epigenetic mechanism that silences p53-activated transcription, irrespective of p53 phosphorylation and stabilization. We show that another adenoviral protein, E4-ORF3, inactivates p53 independently of E1B-55k by forming a nuclear structure that induces de novo H3K9me3 heterochromatin formation at p53 target promoters, preventing p53-DNA binding. This suppressive nuclear web is highly selective in silencing p53 promoters and operates in the backdrop of global transcriptional changes that drive oncogenic replication. These findings are important for understanding how high levels of wild-type p53 might also be inactivated in cancer as well as the mechanisms that induce aberrant epigenetic silencing of tumour-suppressor loci. Our study changes the longstanding definition of how p53 is inactivated in adenovirus infection and provides key insights that could enable the development of true p53-selective oncolytic viral therapies.