Zika virus (ZIKV) infection during human pregnancy may lead to severe fetal pathology and debilitating impairments in offspring. However, the majority of infections are subclinical and not associated with evident birth defects. Potentially detrimental life-long health outcomes in asymptomatic offspring evoke high concerns. Thus, animal models addressing sequelae in offspring may provide valuable information. To induce subclinical infection, we inoculated selected porcine fetuses at the mid-stage of development. Inoculation resulted in trans-fetal virus spread and persistent infection in the placenta and fetal membranes for two months. Offspring did not show congenital Zika syndrome (e.g., microcephaly, brain calcifications, congenital clubfoot, arthrogryposis, seizures) or other visible birth defects. However, a month after birth, a portion of offspring exhibited excessive interferon alpha (IFN-α) levels in blood plasma in a regular environment. Most affected offspring also showed dramatic IFN-α shutdown during social stress providing the first evidence for the cumulative impact of prenatal ZIKV exposure and postnatal environmental insult. Other eleven cytokines tested before and after stress were not altered suggesting the specific IFN-α pathology. While brains from offspring did not have histopathology, lesions, and ZIKV, the whole genome expression analysis of the prefrontal cortex revealed profound sex-specific transcriptional changes that most probably was the result of subclinical in utero infection. RNA-seq analysis in the placenta persistently infected with ZIKV provided independent support for the sex-specific pattern of in utero-acquired transcriptional responses. Collectively, our results provide strong evidence that two hallmarks of fetal ZIKV infection, altered type I IFN response and molecular brain pathology can persist after birth in offspring in the absence of congenital Zika syndrome.