Exposure to endocrine-disrupting chemicals during critical windows of development may lead to functional abnormalities in adulthood. Isoflavones are a flavonoid group of phytoestrogens that are recognized by their estrogenic activity and are highly abundant in soybean. Since the thyroid gland presents estrogen receptors and infants, toddlers and teenagers may consume isoflavones from soy-based infant formula and beverages as alternatives to animal milk, we propose to investigate the potential effects of relevant concentrations of soy isoflavones in the regulation of the hypothalamic–pituitary (HP) thyroid axis using peripubertal male rats as an experimental model. Thirty-two 23-day-old male rats were exposed to 0.5, 5, or 50 mg of soy isoflavones/kg from weaning to 60 days of age, when they were euthanized, and the tissues were collected to evaluate the mRNA expression of genes involved in the regulation of the HP thyroid axis and dosages of thyroid hormones (THs). Serum TSH concentrations were increased, while alterations were not observed in serum concentrations of triiodothyronine and thyroxine. Regarding mRNA gene expression, Mct-8 was increased in the hypothalamus, Mct-8, Thra1, and Thrb2 were decreased in the pituitary, and Nis and Pds were reduced in the thyroid. In the heart, Mct8 and Thrb2 were increased, and Thra1 was decreased. In the liver, Mct8, Thra1, and Thrb2 were decreased. These results suggest that the consumption of relevant doses of soy isoflavones during the peripubertal period in males may induce subclinical hypothyroidism, with alterations in the regulation of the HP thyroid axis, modulation of TH synthesis, and peripheral alterations in TH target organs.