Essential oils from plants are a potential source of molecules having anti-inflammatory, anticancer, cardiotropic, and other activities. However, most of these effects lack mechanistic explanations and structure–activity relationship testing. In the present study, we: 1) identified the nutmeg essential oil (NEO) composition; 2) using molecular docking, we determined the putative regulatory binding sites on the connexin 43 (Cx43) that is responsible for gap junction-dependent intercellular communication (GJIC) in the majority of tissues; 3) examined the effect of NEO and its three constituents – sabinene, α-pinene, and α-copaene – on GJ conductance and gating in Novikoff cells expressing endogenous Cx43; and 4) verified whether NEO effects on GJIC correlated with its action on Novikoff cell viability, proliferation, and colony formation capability. Our results revealed NEO and its constituents as potent and efficient Cx43 GJ inhibitors acting by slow gating mechanism. In addition, NEO reduced Novikoff hepatoma cell viability, proliferation, and colony formation capability; however, this was achieved at higher doses and was unrelated to its effects on GJIC.