A medical device for the separation of a concentrate enriched with cells from a biological fluid, in particular a concentrate of stromal or stem cells from medullar aspirate or venous blood, comprises: - a treatment container (3) for receiving and treating the biological fluid for the purposes of its separation into a number of fractions; - a first collection container (4), for receiving a first fraction of the fluid, in particular a fraction poor in said cells; - a second collection container (5), for receiving a second concentrated fraction of the fluid enriched with said cells; - a deviator valve (7) having a first way connected or prearranged for connection to the treatment container (3), a second way connected or prearranged for connection to the first collection container (4), and a third way connected or prearranged for connection to the second collection container (5); - a first line (10a) for connection of the treatment container (3) to the first way of the deviator valve (7), a second line (4a) for connection of the first collection container (4) to the second way of the deviator valve (7), and a third line for connection of the second collection container (5) with the third way of the deviator valve (7). The treatment container (3) is a syringe container with a plunger having a plunger stem (3c) associated in a releasable way to a corresponding plunger head, and the first connection line comprises a first transparent tube (10a), in particular a flexible transparent tube, and at least one of the second and third connection lines preferably comprises a second flexible tube (4a). At least one connection line, or each connection line, further comprises: at least one respective hydraulic connector (11, 13), for separable connection of a corresponding tube (10a, 4a) to the corresponding container (3, 4, 5) and/or to the corresponding way (7b, 7c, 7d) of the deviator valve (7); and at least one automatic-closing or one-way valve (12, 14a, 14b).