Arenaviruses can cause mild to severe hemorrhagic fevers. Humans mainly get infected through contact with infected rodents or their excretions, yet little is known about transmission dynamics within rodent populations. Morogoro virus (MORV) is an Old World arenavirus closely related to Lassa virus with which it shares the same host species Mastomys natalensis. We injected MORV in its host, and sampled blood and excretions at frequent intervals. Infection in adults was acute; viral RNA disappeared from blood after 18 days post infection (dpi) and from excretions after 39 dpi. Antibodies were present from 7 dpi and never disappeared. Neonatally infected animals acquired a chronic infection with RNA and antibodies in blood for at least 3 months. The quantified excretion and antibody patterns can be used to inform mathematical transmission models, and are essential for understanding and controlling transmission in the natural rodent host populations.