The evolution of a Landau Fermi liquid into a non-magnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics1–6. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids4–7, exciton condensates8 and unconventional superconductivity1. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice9–22, providing a unique opportunity to drive a metal–insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electrically tuning the effective interaction strength in MoTe2/WSe2 moiré superlattices, we observe a continuous MIT at a fixed filling of one electron per unit cell. The existence of quantum criticality is supported by the scaling collapse of the resistance, a continuously vanishing charge gap as the critical point is approached from the insulating side, and a diverging quasiparticle effective mass from the metallic side. We also observe a smooth evolution of the magnetic susceptibility across the MIT and no evidence of long-range magnetic order down to 5% of the Curie–Weiss temperature. This signals an abundance of low-energy spinful excitations on the insulating side that is further corroborated by the Pomeranchuk effect observed on the metallic side. Our results are consistent with the universal critical theory of a continuous Mott transition in two dimensions4,23. © 2021, The Author(s), under exclusive licence to Springer Nature Limited.