The competition between magnetic order and Kondo effect is essential for the rich physics of heavy fermion systems. Nevertheless, how such competition is manifested in the quasiparticle bands in a real periodic lattice remains elusive in spectroscopic experiments. Here we report a high-resolution photoemission study of the antiferromagnetic Kondo lattice system CeCoGe₃ with a high T_N1 of 21 K. Our measurements reveal a weakly dispersive 4f band at the Fermi level near the Z point, arising from a moderate Kondo effect. The intensity of this heavy 4f band exhibits a logarithmic increase with lowering temperature and begins to deviate from this Kondo-like behavior below ∼25 K, just above T_N1, and eventually ceases to grow below ∼12 K. Our work provides direct spectroscopic evidence for the competition between magnetic order and the Kondo effect in a Kondo lattice system with local-moment antiferromagnetism, indicating a distinct scenario for the microscopic coexistence and competition of these phenomena, which might be related to the real-space modulation.