The genome of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) encodes 16 non-structural (Nsp) and 4 structural proteins. Among the Nsps, Nsp1 inhibits host gene expression and also evades the immune system. This protein has been proposed as a target for vaccine development and also for drug design. Owing to its important role, the current study aimed to identify mutations in Nsp1 and their effect on protein stability and flexibility. This is the first comprehensive study in which 295,000 complete genomes have been screened for mutations after alignment with the Wuhan-Hu-1 reference genome (Accession NC_045512), using the CoVsurver app. The sequences harbored 933 mutations in the entire coding region of Nsp1. The most frequently occurring mutation in the 180-amino-acid Nsp1 protein was R24C (n = 1122), followed by D75E (n = 890), D48G (n = 881), H110Y (n = 860), and D144A (n = 648). Among the 933 non-synonymous mutations, 529 exhibited a destabilizing effect. Similarly, a gain in flexibility was observed in 542 mutations. The majority of the most frequent mutations were detected in the loop regions. These findings imply that Nsp1 mutations might be useful to exploit SARS-CoV-2′s pathogenicity. Genomic sequencing of SARS-CoV-2 on a regular basis will further assist in analyzing variations among the drug targets and to test the diagnostic accuracy. This wide range of mutations and their effect on Nsp1’s stability may have some consequences for the host’s innate immune response to SARS-CoV-2 infection and also for the vaccines’ efficacy. Based on this mutational information, geographically strain-specific drugs, vaccines, and antibody combinations could be a useful strategy against SARS-CoV-2 infection.