In silico predictive software allows assessing the effect of amino acid substitutions on the structure or function of a protein without conducting functional studies. The accuracy of in silico pathogenicity prediction tools has not been previously assessed for variants associated with autosomal recessive deafness 1A (DFNB1A). Here, we identify in silico tools with the most accurate clinical significance predictions for missense variants of the GJB2 (Cx26), GJB6 (Cx30), and GJB3 (Cx31) connexin genes associated with DFNB1A. To evaluate accuracy of selected in silico tools (SIFT, FATHMM, MutationAssessor, PolyPhen-2, CONDEL, MutationTaster, MutPred, Align GVGD, and PROVEAN), we tested nine missense variants with previously confirmed clinical significance in a large cohort of deaf patients and control groups from the Sakha Republic (Eastern Siberia, Russia): Сх26: p.Val27Ile, p.Met34Thr, p.Val37Ile, p.Leu90Pro, p.Glu114Gly, p.Thr123Asn, and p.Val153Ile; Cx30: p.Glu101Lys; Cx31: p.Ala194Thr. We compared the performance of the in silico tools (accuracy, sensitivity, and specificity) by using the missense variants in GJB2 (Cx26), GJB6 (Cx30), and GJB3 (Cx31) genes associated with DFNB1A. The correlation coefficient (r) and coefficient of the area under the Receiver Operating Characteristic (ROC) curve as alternative quality indicators of the tested programs were used. The resulting ROC curves demonstrated that the largest coefficient of the area under the curve was provided by three programs: SIFT (AUC = 0.833, p = 0.046), PROVEAN (AUC = 0.833, p = 0.046), and MutationAssessor (AUC = 0.833, p = 0.002). The most accurate predictions were given by two tested programs: SIFT and PROVEAN (Ac = 89%, Se = 67%, Sp = 100%, r = 0.75, AUC = 0.833). The results of this study may be applicable for analysis of novel missense variants of the GJB2 (Cx26), GJB6 (Cx30), and GJB3 (Cx31) connexin genes.