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We report the observation of giant Zeeman shifts in the optical transitions of high-quality very thin films of yttrium iron garnet (YIG) grown by rf sputtering on gadolinium gallium garnet substrates. The optical absorption profile measured with magneto-optical absorption spectroscopy shows dual optical transition in the UV-visible frequency region attributed to transitions from the O-2p valence band to the Fe-3d conduction band and from the O-2p valence band to Fe-2p53d6 excitonic states at the Γ-symmetry point of the YIG band structure. The application of a static magnetic field of only 0.6 kOe produces giant Zeeman shifts of ∼100 meV in the YIG band structure and ∼60 meV in the excitonic states corresponding to effective g-factors on the order of 104. The giant Zeeman effects are attributed to changes in energy levels by the large exchange fields of the Fe-3d orbitals during the magnetization process.