Kaposi sarcoma-associated herpesvirus (KSHV) is an oncogenic γ-herpesvirus. Autophagy during KSHV entry has remained unexplored. We show that LC3 lipidation as a hallmark of autophagy is induced shortly after KSHV entry. LC3 co-localizes with KSHV in amphisomes during entry and loss of LC3 lipidation increases infection. Accordingly, NDP52, a receptor of selective autophagy, was recruited to endocytosed viral particles, and its reduction increased KSHV infection. Additionally, virus particles co-localized with the endolysosome damage sensor galectin-8 upon KSHV entry and depletion of galectin-8 promoted KSHV infection. Compared with herpes simplex virus, listeriolysin, adenovirus, and influenza virus, and in contrast to what was previously thought about enveloped viruses, KSHV binding to EphA2 by its envelope protein gH causes endolysosomal membrane damage, akin to non-enveloped viruses and bacteria. Taken together, our study identifies an important anti-viral role for galectin-8, NDP52, and the autophagy machinery at virus-damaged endosomes, restricting KSHV entry by selective autophagy.