A heat-shrinkable anti-fomitic device in the form of a bag or tube forms a cover for an object which prevents cross-infection by bacteria and other pathogens that may reside on the object. The heat-shrinkable anti-fomitic device can have a sterile interior that is sealed or stored flat during manufacture to maintain sterility. Therefore, no outer wrapping for the anti-fomitic device is required. The anti-fomitic device is inverted when used to cover the object and results in an ultimate outer surface that is initially sterile. A plurality of such devices can be heat shrunk to an object such that removal of the outer layer will prevent cross contamination. Heat shrink film materials for the coverings/bags serve as a barrier to the transmission of pathogens.