SARS-CoV-2 non-structural protein 1 (Nsp1) is a virulence factor that inhibits the innate immune response and translation of host mRNAs. Despite the relevance of Nsp1, few studies have been conducted to understand the effect of mutations on Nsp1 structure and function. Here, we provide a molecular dynamics simulation of SARS-CoV-2 and SARS-CoV-1 Nsp1 conformational changes. Our data supports the idea that SARS-CoV-2 Nsp1 has a less compact structure than SARS-CoV-1 Nsp1. Moreover, several mutations in the helix-loop-helix motif of Nsp1 C-terminal that may affect the interactions of the Nsp1-ribosome complex were investigated. Disordered regions in Nsp1 probably affect host-virus interactions, cross-species transmission, and virus-host range. Overall, these findings reinforce the importance of studying Nsp1 conformational changes in new variants and its effect on virulence of SARS-CoV-2, by altering inhibition potency of host mRNA translation efficiency.