N-myristoylation (Myr) is an eukaryotic N-terminal co- or post-translational protein modification in which the enzyme N-myristoyltransferase (NMT) transfers a fatty acid (C14:0) to the N-terminal glycine residues of several cellular key proteins. Depending on the cellular context, NMT may serve as a molecular target in anticancer or anti-infectious therapy, and drugs that inhibit this enzyme may be useful in the treatment of cancer or infectious diseases. As part of an on-going project to identify natural Homo sapiens N-myristoyltransferase 1 inhibitors (HsNMT1), two ellagitannins, punicalagin (1) and isoterchebulin (2), along with eschweilenol C (3) and ellagic acid (4) were isolated from the bark of Terminalia bentzoë (L.) L. f. subsp. bentzoë. Their structures were determined by means of spectroscopic analyses and comparison with literature data. Punicalagin (1) and isoterchebulin (2) showed significant inhibitory activity towards HsNMT1, and also against Plasmodium falciparum NMT (PfNMT) both in vitro and in cellulo, opening alternative paths for new NMT inhibitors development. This is the first report identifying natural products from a botanical source as inhibitors of HsNMT and PfNMT.