The gradual upscaling of horizontal axis wind turbines has posed major engineering challenges, among which a higher susceptibility of blades and towers to aeroelastic instabilities such as vortex induced vibrations. This work is motivated by the need to develop effective mitigation strategies for this problem. In particular, the use of Locally Resonant Acoustic Metamaterials (LRAM) is proposed. LRAM consist of a regular array of lightweight repeating unit cells, each containing one or more resonators that can respond dynamically to external forcing. This functionality can be achieved through periodic microstructures applied on the surface, or by embedding unit cells within a lattice structure. As a first step to assess the potential of LRAM for mitigating wind turbine aeroelastic instabilities, the present study considers a simplified representation of the targeted mechanism. A numerical model is built around the classical two-dimensional configuration of a transversally oscillating section mounted elastically. Representative operating conditions for wind turbines are considered, and numerical models are set up for both the fluid and the structural subsystems. A partitioned fluid-structure interaction strategy is then employed to solve the coupled problem. The manuscript investigates the influence of the proposed metamaterial on the aeroelastic mechanism and illustrates the potential of this approach for vibration mitigation, while also highlighting its limitations.