A digital ferromagnetic heterostructure composed of a δ-doped layer of Mn in a Ge substrate (Mn/Ge-DFH) has been studied by using the density-functional theory within the generalized gradient approximation. We found that the ferromagnetic order in the Mn layer of the DFH is more favored than the antiferromagnetic order. However, the DFH exhibits metallic behaviors due to the small gap of the host semiconductor. In the majority spin channel, the hole carriers are originated from the hybridized states between the d t2g states of the Mn atom and the p state of its nearest neighbor Ge atoms. These hole states form three bands and are responsible for the ferromagnetic order. In the minority spin channel, the Fermi level is located below the valence band maximum of the host semiconductor, which gives rise to a number of hole carriers with the opposite spin direction in the host. We present the total and partial density of states and the band structures of the two spin channels. By fitting the exchange parameters, we predict the Curie temperature of this DFH.