Random weakening of an intracranial blood vessel results in abnormal blood flow into an aneurysmal sac. Recent advancements show that an implantable flow diverter, integrated with a medical stent, enables a highly effective treatment of cerebral aneurysms by guiding blood flow into the normal vessel path. None of such treatment systems, however, offers post-treatment monitoring to assess the progress of sac occlusion. Therefore, physicians rely heavily on either angiography or magnetic resonance imaging. Both methods require a dedicated facility with sophisticated equipment settings and time-consuming, cumbersome procedures. In this paper, we introduce an implantable, stretchable, nanostructured flow-sensor system for quantification of intra-aneurysmal hemodynamics. The open-mesh membrane device is capable of effective implantation in complex neurovascular vessels with extreme stretchability (500% radial stretching) and bendability (180 with 0.75 mm radius of curvature) for monitoring of the treatment progress. A collection of quantitative mechanics, fluid dynamics, and experimental studies establish the fundamental aspects of design criteria for a highly compliant, implantable device. Hemocompatibility study using fresh ovine blood captures the device feasibility for long-term insertion in a blood vessel, showing less platelet deposition compared to that in existing implantable materials. In vitro demonstrations of three types of flow sensors show quantification of intra-aneurysmal blood flow in a pig aorta and the capability of observation of aneurysm treatment with a great sensitivity (detection limit as small as 0.032 m/s). Overall, this work describes a mechanically soft flow-diverter system that offers an effective treatment of aneurysms with an active monitoring of intra-aneurysmal hemodynamics.