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Cubic spinel GeNi₂O₄ exhibits intriguing magnetic properties with two successive antiferromagnetic phase transitions (~12 and 11 K) in the absence of structural distortion. By means of heat capacity and magnetic susceptibility measurements, we have revealed a new magnetic phase in presence of magnetic field field (≥ 4 T) along the [111] direction, which is not observed when the magnetic field is applied along the [100] and [110] directions. Neutron powder diffraction measurements confirm such a field-induced phase transition and suggest it be ascribed to a spin reorientation in presence of magnetic field. We will discuss the potential mechanisms regarding such a peculiar magnetic anisotropy in this cubic system.