Zika virus (ZIKV) has emerged as an important global health threat, with the recently acquired capacity to cause severe neurological symptoms and to persist within host tissues. We previously demonstrated that an early Asian lineage ZIKV isolate induces a highly activated CD8 T cell response specific for an immunodominant epitope in the ZIKV envelope protein in wild-type mice. Here we show that a contemporary ZIKV isolate from the Brazilian outbreak severely limits CD8 T cell immunity in mice and blocks generation of the immunodominant CD8 T cell response. This is associated with a more sustained infection that is cleared between 7- and 14-days post-infection. Mechanistically, we demonstrate that infection with the Brazilian ZIKV isolate reduces the cross-presentation capacity of dendritic cells and fails to fully activate the immunoproteasome. Thus, our study provides an isolate-specific mechanism of host immune evasion by one Brazilian ZIKV isolate, which differs from the early Asian lineage isolate and provides potential insight into viral persistence associated with recent ZIKV outbreaks.