Arenaviruses and coronaviruses include several human pathogenic viruses, such as Lassa virus, Lymphocytic choriomeningitis virus (LCMV), SARS-CoV, MERS-CoV, and SARS-CoV-2. Although these viruses belong to different virus families, they possess a common motif, the DED/EDh motif, known as an exonuclease (ExoN) motif. In this study, proof-of-concept studies, in which the DED/EDh motif in these viral proteins, NP for arenaviruses, and nsp14 for coronaviruses, could be a drug target, were performed. Docking simulation studies between two structurally different chemical compounds, ATA and PV6R, and the DED/EDh motifs in these viral proteins indicated that these compounds target DED/EDh motifs. The concentration which exhibited modest cell toxicity was used with these compounds to treat LCMV and SARS-CoV-2 infections in two different cell lines, A549 and Vero 76 cells. Both ATA and PV6R inhibited the post-entry step of LCMV and SARS-CoV-2 infection. These studies strongly suggest that DED/EDh motifs in these viral proteins could be a drug target to combat two distinct viral families, arenaviruses and coronaviruses.