Alphaviruses such as Chikungunya and Ross River (RRV) viruses are associated with persistent arthritis and arthralgia in humans. Monocytes and macrophages are believed to play an important role in alphaviral arthritides. In this study, we evaluated RRV permissiveness of the human acute leukemia MM6 cell line. Viral growth analysis showed that RRV infection of MM6 cells resulted in a very low virus progeny production with daily output. Using recombinant RRV expressing the reporter gene Renilla luciferase, a weak viral replication level was detected in infected cells at the early stages of infection. The infection restriction was not associated with type-I interferon and pro-inflammatory cytokines release. Apoptosis hallmarks (i.e. mitochondrial BAX localisation and PARP cleavage) were observed in infected MM6 cells indicating that RRV can trigger apoptosis at late infection times. The long-term persistence of RRV genomic RNA in surviving MM6 cells identifies human monocytic cells as potential cellular reservoirs of viral material within the infected host.