This letter proposes a novel distributed compressed estimation scheme for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive sensing to perform distributed compressed estimation. A design procedure is also presented and an algorithm is developed to optimize measurement matrices, which can further improve the performance of the proposed distributed compressed estimation scheme. Simulations for a wireless sensor network illustrate the advantages of the proposed scheme and algorithm in terms of convergence rate and mean square error performance.