Tissue homeostasis is dependent on the controlled localization of specific cell types and the correct composition of the extracellular stroma. While the role of the cancer stroma in tumour progression has been well characterized, the specific contribution of the matrix itself is unknown. Furthermore, the mechanisms enabling normal-not cancer-stroma to provide tumour-suppressive signals and act as an antitumorigenic barrier are poorly understood. Here we show that extracellular matrix (ECM) generated by normal fibroblasts (NFs) is softer than the CAF matrix, and its physical and structural features regulate cancer cell proliferation. We find that normal ECM triggers downregulation and nuclear exit of the histone demethylase JMJD1a resulting in the epigenetic growth restriction of carcinoma cells. Interestingly, JMJD1a positively regulates transcription of many target genes, including YAP/TAZ (WWTR1), and therefore gene expression in a stiffness-dependent manner. Thus, normal stromal restricts cancer cell proliferation through JMJD1a-dependent modulation of gene expression.