Ebola virus (EBOV) persistence in asymptomatic humans and Ebola virus disease (EVD) sequelae have emerged as significant public health concerns since the 2013-2016 EVD outbreak in Western Africa. Until now, studying how EBOV disseminates into and persists in immune-privileged sites was impossible due to the absence of a suitable animal model. Here, we detect persistent EBOV replication coinciding with systematic inflammatory responses in otherwise asymptomatic rhesus monkeys that had survived infection in the absence of or after treatment with candidate medical countermeasures. We document progressive EBOV dissemination into the eyes, brain and testes through vascular structures, similar to observations in humans. We identify CD68+ cells (macrophages/monocytes) as the cryptic EBOV reservoir cells in the vitreous humour and its immediately adjacent tissue, in the tubular lumina of the epididymides, and in foci of histiocytic inflammation in the brain, but not in organs typically affected during acute infection. In conclusion, our data suggest that persistent EBOV infection in rhesus monkeys could serve as a model for persistent EBOV infection in humans, and we demonstrate that promising candidate medical countermeasures may not completely clear EBOV infection. A rhesus monkey model may lay the foundation to study EVD sequelae and to develop therapies to abolish EBOV persistence.