One of important challenges in condensed-matter physics is to realize new quantum states of matter by manipulating the dimensionality of materials, as represented by the discovery of high-temperature superconductivity in atomic-layer pnictides and room-temperature quantum Hall effect in graphene. Transition-metal dichalcogenides (TMDs) provide a fertile platform for exploring novel quantum phenomena accompanied by the dimensionality change, since they exhibit a variety of electronic/magnetic states owing to quantum confinement. Here we report an anomalous metal-insulator transition induced by three-dimensional (3D)–two-dimensional (2D) crossover in monolayer 1T-VSe₂ grown on bilayer graphene. We observed a complete insulating state with a finite energy gap on the entire Fermi surface in monolayer 1T-VSe₂ at low temperatures, in sharp contrast to metallic nature of bulk. More surprisingly, monolayer 1T-VSe₂ exhibits a pseudogap with Fermi arc at temperatures above the charge-density-wave temperature, showing a close resemblance to high-temperature cuprates. This similarity suggests a common underlying physics between two apparently different systems, pointing to the importance of charge/spin fluctuations to create the novel electronic states, such as pseudogap and Fermi arc, in these materials.