A tubular electromagnetic shielding sleeve has a longitudinal slit. The inventive sleeve includes a substrate (11) and a layer (12) of electrically-conductive material which is fixed to the inner face of the substrate (11), the layer (12) extending essentially from one edge (11a) to the other longitudinal edge (11b) of the substrate (11). Moreover, the substrate (11) and the layer (12) are separated from one another along a split segment (13) on at least one first longitudinal edge (11a). The invention can be used, for example, to protect bundles of electric cables (14) for use in aeronautics.