High-temperature superconductivity in cuprates emerges upon doping the parent Mott insulator. Key features of the low-doped cuprate superconductors include an effective carrier density that tracks the number of doped holes, the emergence of an anisotropic pseudogap that is characterized by disconnected Fermi arcs, and the closure of the gap at a critical doping level. In Sr₂IrO₄, a spin–orbit-coupled Mott insulator often regarded as a 5d analog of the cuprates, surface probes have also revealed the emergence of an anisotropic pseudogap and Fermi arcs under electron doping. However, neither the corresponding critical doping nor the bulk signatures of pseudogap closure have yet been observed. Here we demonstrate that electron-doped Sr₂IrO₄ exhibits a critical doping level with a marked crossover in the effective carrier density at low temperatures. This is accompanied by a five-orders-of-magnitude increase in conductivity and a sixfold enhancement in the electronic-specific heat. These collective findings resemble the bulk pseudogap phenomenology in cuprates. However, given that electron-doped Sr₂IrO₄ is non-superconducting, it suggests that the pseudogap may not be a state of precursor pairing. Therefore, our results narrow the search for the key ingredient underpinning the formation of the superconducting condensate in doped Mott insulators.