Adeno-associated virus (AAV) vectors are one of the leading platforms for gene delivery for the treatment of human genetic diseases, but the antiviral cellular mechanisms that interfere with optimal transgene expression are incompletely understood. Here, we performed two genome-scale CRISPR screens to identify cellular factors that restrict transgene expression from AAV vectors. Our screens revealed several components linked to DNA damage response, chromatin remodeling and transcriptional regulation. Inactivation of the Fanconi Anemia gene FANCA, the Human Silencing Hub (HUSH) associated methyltransferase SETDB1 and the gyrase, Hsp90, histidine kinase and MutL (GHKL)-type ATPase MORC3 led to increased transgene expression. Moreover, SETDB1 and MORC3 knockout improved transgene levels of several AAV serotypes as well as other viral vectors, such as Lentivirus and Adenovirus. Finally, we demonstrated that siRNA knockdown of SETDB1 and MORC3 prior to viral vector administration enhanced transgene expression, providing a strategy for the improvement of gene therapy applications.