Clinical reports of Zika Virus (ZIKV) RNA detection in breast milk have been described, but evidence conflicts as to whether this RNA represents infectious virus. We infected post-parturient AG129 murine dams deficient in type I and II interferon receptors with ZIKV. ZIKV RNA was detected in pup stomach milk clots (SMC) as early as 1 day post maternal infection (dpi) and persisted as late as 7 dpi. In mammary tissues, ZIKV replication was demonstrated by immunohistochemistry in multiple cell types including cells morphologically consistent with myoepithelial cells. No mastitis was seen histopathologically. In the SMC and tissues of the nursing pups, no infectious virus was detected via focus forming assay. However, serial passages of fresh milk supernatant yielded infectious virus, and immunohistochemistry showed ZIKV replication protein associated with degraded cells in SMC. These results suggest that breast milk may contain infectious ZIKV. However, breast milk transmission (BMT) does not occur in this mouse strain that is highly sensitive to ZIKV infection. These results suggest a low risk for breast milk transmission of ZIKV, and provide a platform for investigating ZIKV entry into milk and mechanisms which may prevent or permit BMT.