Layered 5d transition metal oxides (TMOs) have attracted significant interest in recent years because of the rich physical properties induced by the interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion. In Sr2IrO4, this interplay opens a gap near the Fermi energy and stabilizes a Jeff=1/2 spin-orbital entangled insulating state at low temperatures. Whether this metal-insulating transition (MIT) is Mott-type (electronic-correlation driven) or Slater-type (magnetic-order driven) has been under intense debate. We address this issue via spatially resolved imaging and spectroscopic studies of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy (STM/S). The STS results clearly illustrate the opening of the (~150-250 meV) insulating gap at low temperatures, in qualitative agreement with our density-functional theory (DFT) calculations. More importantly, the measured temperature dependence of the gap width coupled with our DFT+dynamical mean field theory (DMFT) results strongly support the Slater-type MIT scenario in Sr2IrO4. The STS data further reveal a pseudogap structure above the Neel temperature, presumably related to the presence of antiferromagnetic fluctuations.