Prenatal hypoxia (PH) is a major cause of nervous system disorders in early childhood, leading to reduced learning and memory capabilities, increased anxiety, and a higher risk of developing mental and neurodegenerative diseases later in life. Compensatory-adaptive mechanisms of the mother-placenta-fetus system, which enhance the fetus’s CNS resilience, are known, including the activation of endogenous neuroprotection in response to hypoxic brain injury through pharmacological modulation of HSP70. To evaluate the effect of HSP70 modulators—Cerebrocurin, Angiolin, Tamoxifen, Glutaredoxin, Thiotriazoline, HSF-1 (heat shock factor 1 protein), as well as Mildronate and Mexidol—on motor, exploratory, psycho-emotional activity, learning, and memory of offspring after PH. Experimental PH was induced by daily intraperitoneal injections of sodium nitrite solution to pregnant female rats from the 16th to the 21st day of pregnancy at a dose of 50 mg/kg. Newborns received intraperitoneal injections of Angiolin (50 mg/kg), Thiotriazoline (50 mg/kg), Mexidol (100 mg/kg), Cerebrocurin (150 µL/kg), L-arginine (200 mg/kg), Glutaredoxin (200 µg/kg), HSF-1 (50 mg/kg), and Mildronate (50 mg/kg) for 30 days. At 1 month, rats were tested in the open field test, and at 2 months, they were trained and tested for working and spatial memory in the radial maze. Modeling PH led to persistent impairments in exploratory activity, psycho-emotional behavior, and a decrease in cognitive-mnestic functions of the CNS. It was found that Angiolin and Cerebrocurin had the most pronounced effects on the indicators of exploratory-activity and psycho-emotional status in 1-month-old animals after PH. They also exhibited the most significant cognitive-enhancing and memory-supporting effects during training and evaluation of skill retention in the maze in 2-month-old offspring after PH. The obtained results provide experimental justification for further research into Angiolin and Cerebrocurin as promising neuroprotective agents for use after PH. Obtained results will help to expand our understanding of the effect of beta-blockers of various generations used to treat cardiovascular diseases on energy metabolism, and are also an experimental justification for the practical choice of these drugs in the complex therapy of CHF.