Despite the improvements in biotechnological approaches and the selection of controlled ovarian hyperstimulation protocols, the resulting pregnancy rate from in vitro fertilization (IVF) protocols still does not exceed 30–40%. In this connection, there is an acute question of the development of a non-invasive, sensitive, and specific method for assessing the implantation potential of an embryo. A total of 110 subfertile couples were included in the study to undergo the IVF/ICSI program. Obtained embryos for transfer into the uterine cavity of patient cohort 1 (n = 60) and cohort 2 (n = 50) were excellent/good-quality blastocysts, and small noncoding RNA (sncRNA) content in the corresponding spent culture medium samples at the morula stage (n = 43) or at the blastocyst stage (n = 31) was analyzed by deep sequencing followed by qRT-PCR in real time. Two logistic regression models were developed to predict the implantation potential of the embryo with 100% sensitivity and 100% specificity: model 1 at the morula stage, using various combinations of hsa_piR_022258, hsa-let-7i-5p, hsa_piR_000765, hsa_piR_015249, hsa_piR_019122, and hsa_piR_008112, and model 2 at the blastocyst stage, using various combinations of hsa_piR_020497, hsa_piR_008113, hsa-miR-381-3p, hsa_piR_022258, and hsa-let-7a-5p. Protein products of sncRNA potential target genes participate in the selective turnover of proteins through the ubiquitination system and in the organization of the various cell cytoskeleton and nucleoskeleton structures, regulating the activity of the Hippo signaling pathway, which determines the fate specification of the blastomers.