The ongoing COVID-19 pandemic has resulted in a global panic because of its continual evolution and recurring spikes. This serious malignancy is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the outbreak, millions of people have been affected from December 2019 till now, which has led to a great surge in finding treatments. Despite trying to handle the pandemic with the repurposing of some drugs, such as chloroquine, hydroxychloroquine, remdesivir, lopinavir, ivermectin, etc., against COVID-19, the SARS-CoV-2 virus continues its out-of-control spread. There is a dire need to identify a new regimen of natural products to combat the deadly viral disease. This article deals with the literature reports to date of natural products showing inhibitory activity towards SARS-CoV-2 through different approaches, such as in vivo, in vitro, and in silico studies. Natural compounds targeting the proteins of SARS-CoV-2—the main protease (Mpro), papain-like protease (PLpro), spike proteins, RNA-dependent RNA polymerase (RdRp), endoribonuclease, exoribonuclease, helicase, nucleocapsid, methyltransferase, adeno diphosphate (ADP) phosphatase, other nonstructural proteins, and envelope proteins—were extracted mainly from plants, and some were isolated from bacteria, algae, fungi, and a few marine organisms.