The present invention provides a removable and disposable fitted plastic enclosure or cover for covering a shopping cart handle or a luggage cart handle for cleanliness. The plastic enclosure has two closed sides, three closed edges, and one open side for snuggly receiving in the enclosure a handle of a shopping cart or a luggage cart. The two closed sides preferably include two rectangular shaped sides facing each other for covering and enclosing the handle. The three edges include three narrow surrounding closed edges to form the enclosure. Further, a plurality of enclosures are detachably connected in and end-to-end relationship to form a continuous roll of detachable plastic enclosures, which are disposable after use.