The discovery of two-dimensional (2D) magnetism combined with van der Waals (vdW) heterostructure engineering offers unprecedented opportunities for creating artificial magnetic structures with non-trivial magnetic textures. Further progress hinges on deep understanding of electronic and magnetic properties of 2D magnets at the atomic scale. Although local electronic properties can be probed by scanning tunneling microscopy/spectroscopy (STM/STS), its application to investigate 2D magnetic insulators remains elusive due to absence of a conducting path and their extreme air sensitivity. Here we demonstrate that few-layer CrI3 (FL-CrI3) covered by graphene can be characterized electronically and magnetically via STM by exploiting the transparency of graphene to tunneling electrons. STS reveals electronic structures of FL-CrI3 including flat bands responsible for its magnetic state. AFM-to-FM transition of FL-CrI3 can be visualized through the magnetic field dependent moiré contrast in the dI/dV maps due to a change of the electronic hybridization between graphene and spin-polarised CrI3 bands with different interlayer magnetic coupling. Our findings provide a general route to probe atomic-scale electronic and magnetic properties of 2D magnetic insulators for future spintronics and quantum technology applications.