In one embodiment, the protective cover assembly (11) has a hub (15) that is to be mounted on a needle assembly (10), such as a biopsy needle assembly, a cap (17) that is movable off the hub (15) to move over a cannula (13) or stylet (14) of the needle assembly (10) and a pair of rolls of film (20,21) within the cap (17). The rolls of film (20,21) are secured at one end to the hub (15) to unwind over the cannula (13). Pressing rolls (43) or springs (26) press the longitudinal edges of the film strips together in sealed relation to encase the cannula (13) while the cap (17) receives the end of the cannula (13) or stylet (14) in sealed relation. In a second embodiment, the cap (38) is integrated with a hub (37) of a needle assembly (36) having a cannula (13) extending from the hub (37).