The SARS-CoV-2 non-structural protein 1 (Nsp1) contains an N-terminal domain and C-terminal helices connected by a short linker region. The C-terminal helices of Nsp1 (Nsp1-C-ter) from SARS-CoV-2 bind in the mRNA entry channel of the 40S ribosomal subunit and blocks mRNA entry, thereby shutting down host protein synthesis. Nsp1 suppresses host immune function and is vital for viral replication. Hence, Nsp1 appears to be an attractive target for therapeutics. In this study, we have in silico screened Food and Drug Administration (FDA)-approved drugs against Nsp1-C-ter. Among the top hits obtained, montelukast sodium hydrate binds to Nsp1 with a binding affinity (KD) of 10.8 ± 0.2 µM in vitro. It forms a stable complex with Nsp1-C-ter in simulation runs with –95.8 ± 13.3 kJ/mol binding energy. Montelukast sodium hydrate also rescues the inhibitory effect of Nsp1 in host protein synthesis, as demonstrated by the expression of firefly luciferase reporter gene in cells. Importantly, it shows antiviral activity against SARS-CoV-2 with reduced viral replication in HEK cells expressing ACE2 and Vero-E6 cells. We, therefore, propose montelukast sodium hydrate can be used as a lead molecule to design potent inhibitors to help combat SARS-CoV-2 infection.