The nonstructural proteins 7 and 8 (nsp7 and nsp8) of SARS-CoV-2 are highly important proteins involved in the RNA-dependent polymerase (RdRp) protein replication complex. In this study, we analyzed the global mutation of nsp7 and nsp8 in 2022 and 2023 and analyzed the effects of mutation on the viral replication protein complex using bio-chemoinformatics. Frequently occurring variants are found to be single amino acid mutations for both nsp7 and nsp8. The most frequently occurring mutations for nsp7 which include L56F, L71F, S25L, M3I, D77N, V33I and T83I are predicted to cause destabilizing effects, whereas those in nsp8 are predicted to cause stabilizing effects, with the threonine to isoleucine mutation (T89I, T145I, T123I, T148I, T187I) being a frequent mutation. A conserved domain database analysis generated critical interaction residues for nsp7 (Lys-7, His-36 and Asn-37) and nsp8 (Lys-58, Pro-183 and Arg-190), which, according to thermodynamic calculations, are prone to destabilization. Trp-29, Phe-49 of nsp7 and Trp-154, Tyr-135 and Phe-15 of nsp8 cause greater destabilizing effects to the protein complex based on a computational alanine scan suggesting them as possible new target sites. This study provides an intensive analysis of the mutations of nsp7 and nsp8 and their possible implications for viral complex stability.