The development of the Internet of Things infrastructure requires the deployment of millions of heterogeneous sensors embedded in the environment. The powering of these sensors cannot be done with wired connections, and the use of batteries is often impracticable. Energy harvesting is the common proposed solution, and many devices have been developed for this purpose, using light, mechanical vibrations, and temperature differences as energetic sources. In this paper we present a novel energy-harvester device able to capture the kinetic energy from a fluid in motion and transform it in electrical energy. This device, named FLEHAP (FLuttering Energy Harvester for Autonomous Powering), is based on an aeroelastic effect, named fluttering, in which a totally passive airfoil shows large and regular self-sustained motions (limit cycle oscillations) even in extreme conditions (low Reynolds numbers), thanks to its peculiar mechanical configuration. This system shows, in some centimeter-sized configurations, an electrical conversion efficiency that exceeds 8% at low wind speed (3.5 m/s). By using a specialized electronic circuit, it is possible to store the electrical energy in a super capacitor, and so guarantee self-powering in such environmental conditions.