Epstein-Barr virus (EBV) is an oncogenic herpesvirus that is ubiquitous in the human population. Early after EBV infection in vitro, primary human B cells undergo a transient period of hyper-proliferation, which results in replicative stress and DNA damage, activation of the DNA damage response (DDR) pathway and, ultimately, senescence. In this study, we investigated DDR-mediated senescence in early arrested EBV-infected B cells and characterized the establishment of persistent DNA damage foci. We found that arrested EBV-infected B cells exhibited an increase in promyelocytic leukemia nuclear bodies (PML NBs), which predominantly localized to markers of DNA damage, as well as telomeric DNA. Furthermore, arrested EBV-infected B cells exhibited an increase in the presence of telomere dysfunction-induced foci. Importantly, we found that increasing human telomerase reverse transcriptase (hTERT) expression with danazol, a drug used to treat telomere diseases, permitted early EBV-infected B cells to overcome cellular senescence and enhanced transformation. Finally, we report that EBV-infected B cells undergoing hyper-proliferation are more sensitive than lymphoblastoid cell lines (LCLs) to inhibition of Bloom syndrome-associated helicase, which facilitates telomere replication. Together, our results describe the composition of persistent DNA damage foci in the early stages of EBV infection and define key regulators of this barrier to long-term outgrowth.