A statue of Rostropovich will be placed in central Moscow as a memorial to the cellist and conductor. The monument is set to stand near a 17th-century church not far from the Moscow Conservatoire where Rostropovich studied and taught. The statue is being financed by the Rostropovich Foundation and is set to be unveiled on 27 March 2012, the 85th anniversary of the cellist's birth.

A bronze bust of Rostropovich has stood in Kronberg, Germany, since October 2007. Rostropovich was an artistic adviser of the Kronberg Academy from 1997 until his death in April 2007 and called the town the 'world capital of the cello'. The bronze was paid for by Kronberg citizens.