A cover for a musical instrument, especially but not exclusively a drum, includes a portion formed by inner and outer sheets fastened together to define a pocket that is padded with a desiccating material. Preferably, the inner and outer sheets are quilted to define a plurality of pockets, each of which is tightly stuffed with a granular form of desiccating material. In this way, the cover provides protection for the instrument and also assists in keeping the instrument in tune by removing moisture from air trapped between the instrument and the portion defining the pockets.