A medical unit includes a shielded enclosure (2) in which are accommodated:—elements (13) for supporting a container (12) including a source or a generator of injectable radioactive product (11),—elements (10) for supporting a syringe (6),—a device (3) of the activimeter type, and—a system of pipes (9, 20, 23, 24) associated with at least one valve (15). The syringe support (10), the valve (15) and the radioactive source support (13) are arranged vertically relative to one another, respectively from top to bottom, the syringe support (10) being arranged to support the syringe (6) with the plunger (8) thereof oriented upward. The valve (15) and the syringe plunger (8) can be operated so as to ensure the withdrawal, dilution and injection operations.