Motivated by the recent experimental progress in TI/CrSb heterogeneous film, the magnetic and electronic structures of the Sb2Te3/CrSb heterostructure are investigated through first-principle calculations and a low-energy effective model. Atoms near the interface are magnetized due to the magnetic proximity effect from CrSb. Accordingly, a surface state gap of about 2.4 meV is induced in the band structure. Interestingly, the induced gap can be further tuned from the interface spacing between Sb2Te3 and CrSb, where the energy difference between the two nondegenerate surface Dirac cones plays a role. Our results reveal that the anomalous Hall effect observed in TI/CrSb heterostructure originates from the surface state gap from magnetic introducing. Our study sheds new light on the understanding of the surface state gap in TI/FM (AFM) heterostructures.