The oncolytic autonomous parvovirus Minute Virus of Mice (MVM) establishes infection in the nuclear environment by usurping host DNA damage signaling proteins in the vicinity of cellular DNA break sites. MVM replication induces a global cellular DNA Damage Response (DDR) that is dependent on signaling by the ATM kinase and inactivates the cellular ATR-kinase pathway. However, the mechanism of how MVM generates cellular DNA breaks remains unknown. Using single molecule DNA Fiber Analysis, we have discovered that MVM infection leads to a shortening of host replication forks as infection progresses, as well as induction of replication stress prior to the initiation of virus replication. Ectopically expressed viral non-structural proteins NS1 and NS2 are sufficient to cause host-cell replication stress, as is the presence of UV-inactivated non-replicative MVM genomes. The host single-stranded DNA binding protein Replication Protein A (RPA) associates with the UV-inactivated MVM genomes, suggesting MVM genomes might serve as a sink for cellular stores of RPA. Overexpressing RPA in host cells prior to UV-MVM infection rescues DNA fiber lengths and increases MVM replication, confirming that MVM genomes deplete RPA stores to cause replication stress. Together, these results indicate that parvovirus genomes induce replication stress through RPA exhaustion, rendering the host genome vulnerable to additional DNA breaks.