Eukaryotic genomes are broadly divided between gene-rich euchromatin and the highly repetitive heterochromatin domain, which is enriched for proteins critical for genome stability and transcriptional silencing. This study shows that Drosophila KDM4A (dKDM4A), previously characterized as a euchromatic histone H3 K36 demethylase and transcriptional regulator, predominantly localizes to heterochromatin and regulates heterochromatin position-effect variegation (PEV), organization of repetitive DNAs, and DNA repair. We demonstrate that dKDM4A demethylase activity is dispensable for PEV. In contrast, dKDM4A enzymatic activity is required to relocate heterochromatic double-strand breaks outside the domain, as well as for organismal survival when DNA repair is compromised. Finally, DNA damage triggers dKDM4A-dependent changes in the levels of H3K56me3, suggesting that dKDM4A demethylates this heterochromatic mark to facilitate repair. We conclude that dKDM4A, in addition to its previously characterized role in euchromatin, utilizes both enzymatic and structural mechanisms to regulate heterochromatin organization and functions.