Density matrix embeddingﾠtheoryﾠ[G. Knizia and G. K.-L. Chan,ﾠPhys. Rev. Lett.109, 186404 (2012)] and density embeddingﾠtheoryﾠ[I. W. Bulik, G. E. Scuseria, and J. Dukelsky,ﾠPhys. Rev. Bﾠ89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to theﾠab initioﾠdescription of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, usingﾠcoupled clusterﾠtheoryﾠas the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable toﾠcoupled clusterﾠcalculations of infinite systems even when using a single unit cell as the fragment. Theﾠtheoryﾠis formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.