Prenatal stress can negatively impact neonatal health, growth, and bonding with the mother. However, molecular basis of these modifications is not completely understood. The aim of this experimental study was to test the hypothesis that intrauterine stress exposure may contribute to subsequent depression-like comorbidities associated with neuroinflammation. Wistar Albino nulliparous female rats were divided into two groups (each, n = 6): controls and pregnancy stress (Days 1 through 21). Two live rat pups (one female and one male) from each term delivery were randomly selected, and depression-like behavior tests were performed on Postpartum Days 30–34, followed by euthanasia on Day 35. NOD-, LRR-, and pyrin domain-containing protein 3 (NLRP3) pathway gene expressions in the hippocampus and immunohistochemical caspase 3 (cas-3), mammalian target of rapamycin (mTOR), and transient receptor potential melastatin (TRPM) staining in the temporal and prefrontal cortices were evaluated. Compared with controls, exposure to prenatal stress was associated with increased depression and anxiety-like behavior, hippocampal NLRP3 inflammasome activation (p = 0.022 and p = 0.035 for female and male pups, respectively), neuronal degeneration and increased cas-3, mTOR, and TRPM immunostaining in the prefrontal and temporal cortices of both female and male offspring (p < 0.05 for all comparisons except p < 0.01 for cas-3 in the male cortex and female temporal cortex). Exposure to antenatal stress can lead to depression-like behavior in the infant, mainly driven by hippocampal NLRP3 inflammasome activation, cortical neuroinflammation, and neurodegeneration. Future perspectives include NLRP3-targeted therapies with anti-inflammatory and anti-apoptotic effects against adverse prenatal effects of maternal stress.