Background: In population ecology, the concept of reproductive potential denotes the most vital indicator of chances to produce and sustain a healthy descendant until his/her reproductive maturity under the best conditions. This concept links quality of life and longevity of an individual with disease susceptibilities encoded by his/her genome. Female reproductive potential has been investigated deeply, widely, and comprehensively in the past, but the male one has not received an equal amount of attention. Therefore, here we focused on the human Y chromosome and found candidate single-nucleotide polymorphism (SNP) markers of male reproductive potential. Results: Examining in silico (i.e., using our earlier created Web-service SNP_TATA_Z-tester) all 1206 unannotated SNPs within 70 bp proximal promoters of all 63 Y-linked genes, we found 261 possible male-reproductive-potential SNP markers that can significantly alter the binding affinity of TATA-binding protein (TBP) for these promoters. Among them, there are candidate SNP markers of spermatogenesis disorders (e.g., rs1402972626), pediatric cancer (e.g., rs1483581212) as well as male anxiety damaging family relationships and mother’s and children’s health (e.g., rs187456378). First of all, we selectively verified in vitro both absolute and relative values of the analyzed TBP–promoter affinity, whose Pearson’s coefficients of correlation between predicted and measured values were r = 0.84 (significance p < 0.025) and r = 0.98 (p < 0.025), respectively. Next, we found that there are twofold fewer candidate SNP markers decreasing TBP–promoter affinity relative to those increasing it, whereas in the genome-wide norm, SNP-induced damage to TBP–promoter complexes is fourfold more frequent than SNP-induced improvement (p < 0.05, binomial distribution). This means natural selection against underexpression of these genes. Meanwhile, the numbers of candidate SNP markers of an increase and decrease in male reproductive potential were indistinguishably equal to each other (p < 0.05) as if male self-domestication could have happened, with its experimentally known disruptive natural selection. Because there is still not enough scientific evidence that this could have happened, we discuss the human diseases associated with candidate SNP markers of male reproductive potential that may correspond to domestication-related disorders in pets. Conclusions: Overall, our findings seem to support a self-domestication syndrome with disruptive natural selection by male reproductive potential preventing Y-linked underexpression of a protein.