Summary: Let \(G\) be a graph that is a subgraph of some \(n\)-dimensional hypercube \(Q_n\). For sufficiently large \(n\), \textit{Q. Stout} [``Packings in hypercubes'', presented at the 21st Southeastern international conference on combinatorics, graph theory, and computing, Boca Raton, FL (1990), \url{http://www.eecs.umich.edu/~qstout/abs/hyppack.html}] proved that it is possible to pack vertex-disjoint copies of \(G\) in \(Q_n\) so that any proportion \(r<1\) of the vertices of \(Q_n\) are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large \(n\), it is possible to pack edge-disjoint copies of \(G\) in \(Q_n\) so that any proportion \(r<1\) of the edges of \(Q_n\) are covered by the packing.