The Mammarenavirus genus includes several pathogenic species of rodent-borne viruses. Old World (OW) mammarenaviruses infect rodents in the Murinae subfamily and are mainly transmitted in Africa and Asia; New World (NW) mammarenaviruses are found in rodents of the Cricetidae subfamily in the Americas. We applied a selection-informed method to estimate that OW and NW mammarenaviruses diverged less than ∼45,000 years ago (ya). By incorporating phylogeographic inference, we show that NW mammarenaviruses emerged in the Latin America-Caribbean region ∼41,400-3,300 ya, whereas OW mammarenaviruses originated ∼23,100-1,880 ya, most likely in Southern Africa. Cophylogenetic analysis indicated that cospeciation did not contribute significantly to mammarenavirus-host associations. Finally, we show that extremely strong selective pressure on the viral polymerase accompanied the speciation of NW viruses. These data suggest that the evolutionary history of mammarenaviruses was not driven by codivergence with their hosts. The viral polymerase should be regarded as a major determinant of mammarenavirus adaptation.