Theileria and Babesia species are eukaryotic protozoan parasites classified under the order Piroplasmida of the phylum Apicomplexa. Tick vectors transmit these microorganisms in tropical and subtropical regions to a wide range of animals, including ruminants, causing fatal and life-threatening diseases such as bovine babesiosis and theileriosis. Resistance to commercially available drugs requires the search for new drug candidates. Histone deacetylase (HDAC) has a potential to be utilized as a drug target; therefore, it may be considered as an effective alternative. Previous studies revealed that HDAC inhibitors, identified for human use, show promising anti-parasitic effects. We have herein focused on the class I HDAC enzyme, HDAC1, of the Babesia and Theileria species to discover potential benzamide inhibitors by following a streamlined workflow of computer-aided drug design methodology. Molecular docking and molecular dynamics simulations revealed that benzamide derivatives stably interacted with the HDAC1 active site in both parasites as hypothesized. Furthermore, specific residue insertions at the entry point of the active site cleft of parasitic HDAC1 could enable ways to design parasite-specific drugs without adversely affecting host enzymes.