Recent data in a nonhuman primate model showed that infants postnatally infected with Zika virus (ZIKV) were acutely susceptible to high viremia and neurological damage, suggesting the window of vulnerability extends beyond gestation. In this pilot study, we addressed the susceptibility of two infant rhesus macaques born healthy to dams infected with Zika virus during pregnancy. Passively acquired neutralizing antibody titers dropped below detection limits between 2 and 3 months of age, while binding antibodies remained detectable until viral infection at 5 months. Acute serum viremia was comparatively lower than adults infected with the same Brazilian isolate of ZIKV (n = 11 pregnant females, 4 males, and 4 non-pregnant females). Virus was never detected in cerebrospinal fluid nor in neural tissues at necropsy two weeks after infection. However, viral RNA was detected in lymph nodes, confirming some tissue dissemination. Though protection was not absolute and our study lacks an important comparison with postnatally infected infants born to naïve dams, our data suggest infants born healthy to infected mothers may harbor a modest but important level of protection from postnatally acquired ZIKV for several months after birth, an encouraging result given the potentially severe infection outcomes of this population.