This device (10) includes an implant (20) which has a tubular endoprosthesis (30) with a radially deployable framework (36). The implant (20) includes a flexible interposition member (24) mounted movably on the endoprosthesis (30) so as to be interposed between the outer surface (40) and a blood circulation conduit (14). The device (10) includes a deployment tool (26) which can adopt a configuration for insertion of the implant (20) and a configuration for release of the implant (20). In the configuration for insertion of the implant (20), the flexible member (24) includes at least one free part (68) held axially away from the outer surface (40) in order to minimize the radial dimension of the implant (20). The free part (68) is at least partly displaceable against the outer surface (40) when the tool (26) moves from its configuration for insertion to its configuration for release.
