A cryogenic grinding apparatus is provided. The apparatus includes a material charge, a low-temperature embrittling device for embrittling the charged ground material by supplying liquid low-temperature gas, a mill for grinding the low-temperature embrittled ground material in an atmosphere containing the low-temperature gas, and a separating device. The separating device has a wind classifier, a removal device to remove the ground material from the mill-output volumetric flow, and a directing device to feed the removed ground material into a classifier-input volumetric flow and to discharge excess mill-output gas of the mill-output volumetric flow. In addition, a cryogenic grinding process is provided in which the ground material is removed from the volumetric flow, excess grinding gas is discharged, removed ground material is feed into a classifier-input volumetric flow of a wind classifier and a classifier-input volumetric flow is classified for separating off a classifier-output volumetric flow containing the fine material.