The infrared optical, magneto-optical properties of CoFe2O4 single crystals are considered. The magneto-absorption of natural light in the infrared spectral range in CoFe2O4 spinel is studied in the Voight experimental geometry. This magneto-optical effect is very high and associates with a change in the fundamental absorption edge and impurity absorption bands under a magnetic field. The magneto-absorption strongly depending on both the magnitude and the orientation of the magnetic field relative to the crystallographic axes of the crystal is presented in this paper. The contribution of magnetostriction to the magnetic anisotropy constant of the CoFe2O4 crystal is shown to be abnormally large. The clear connection between magneto-absorption of light in the infrared spectral range and magnetostriction of the CoFe2O4 spinel is established.