(1) Background: Hormone-dependent events that occur throughout spermatogenesis during postnatal testis maturation are significant for adult male fertility. Any disturbances in the T/DHT ratio in male progeny born from females fertilized by finasteride-treated male rats (F0:Fin) can result in the impairment of testicular physiology. The goal of this work was to profile the testicular transcriptome in the male filial generation (F1:Fin) from paternal F0:Fin rats. (2) Methods: The subject material for the study were testis from immature and mature male rats born from females fertilized by finasteride-treated rats. Testicular tissues from the offspring were used in microarray analyses. (3) Results: The top 10 genes having the highest and lowest fold change values were mainly those that encoded odoriferous (Olfr: 31, 331, 365, 633, 774, 814, 890, 935, 1109, 1112, 1173, 1251, 1259, 1253, 1383) and vomeronasal (Vmn1r: 50, 103, 210, 211; Vmn2r: 3, 23, 99) receptors and RIKEN cDNA 5430402E10, also known as odorant-binding protein. (4) Conclusions: Finasteride treatment of male adult rats may cause changes in the testicular transcriptome of their male offspring, leading to a defective function of spermatozoa in response to odorant-like signals, which are recently more and more often noticed as significant players in male fertility.