An implantable device (1) for injecting fluid and/or for tapping fluid, the device having a housing (3) provided with a puncture zone (4) able to be transpierced by a hollow needle (5) for injecting fluid into and/or tapping fluid from a chamber (3A) provided inside the housing (3). The implantable device has a puncture zone (4) made up of at least first and second superposed flexible membranes (6, 7) mounted to be free, at least locally, relative to each other, to allow the membranes, at least locally, to move along each other, so that, once the needle (5) has been removed, the orifice formed by the needle (5) is sliced into first and second sub-orifices (6A, 7A) substantially not coinciding so as to impart a substantially leaktight property to the puncture zone (4).