A paradoxical reduction in anxiety levels in chronic predator stress paradigm (PS) in Sprague–Dawley rats has recently been shown in previous works. In this paper, we studied the possible neurobiological mechanism of this phenomenon. We segregated PS-exposed Sprague–Dawley rats into the high- and low-anxiety phenotypes. The long-lasting effects of PS on corticosterone levels, blood flow speed in the carotid arteries, diffusion coefficient, and 1H nuclear magnetic resonance spectra in the hippocampus were compared in the high-anxiety and low-anxiety rats. In addition, we evaluated the gene BDNF expression in the hippocampus which is considered to be a main factor of neuroplasticity. We demonstrated that in low-anxiety rats, the corticosterone level was decreased and carotid blood flow speed was increased. Moreover, in the hippocampus of low-anxiety rats compared to the control group and high-anxiety rats, the following changes were observed: (a) a decrease in N-acetyl aspartate levels with a simultaneous increase in phosphoryl ethanol amine levels; (b) an increase in lipid peroxidation levels; (c) a decrease in apparent diffusion coefficient value; (d) an increase in BDNF gene expression. Based on these findings, we proposed that stress-induced anxiety reduction is associated with the elevation of BDNF gene expression directly. Low corticosterone levels and a rise in carotid blood flow speed might facilitate BDNF gene expression. Meanwhile, the decrease in apparent diffusion coefficient value and decrease in N-acetyl aspartate levels, as well as an increase in the lipid peroxidation levels, in the hippocampus possibly reflected destructive changes in the hippocampus. We suggested that in Sprague–Dawley rats, these morphological alterations might be considered as an impetus for further increase in neuroplasticity in the hippocampus.