Spinel-type CoFe$_2$O$_4$ is a ferrimagnetic insulator with the Neel temperature exceeding 790 K, and shows a strong cubic magnetocrystalline anisotropy (MCA) in bulk materials. However, when a CoFe$_2$O$_4$ film is grown on other materials, its magnetic properties are degraded so that so-called magnetically dead layers are expected to be formed in the interfacial region. We investigate how the magnetic anisotropy of CoFe$_2$O$_4$ is modified at the interface of CoFe$_2$O$_4$/Al$_2$O$_3$ bilayers grown on Si(111) using x-ray magnetic circular dichroism (XMCD). We find that the thinner CoFe$_2$O$_4$ films have significantly smaller MCA values than bulk materials. The reduction of MCA is explained by the reduced number of Co$^{2+}$ ions at the $O_h$ site reported by a previous study [Y. K. Wakabayashi $textit{et al.}$, Phys. Rev. B $textbf{96}$, 104410 (2017)].
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