In this paper, we propose a novel flexible metamaterial (MM) absorber. The conductive pattern consists of liquid metal eutectic gallium indium alloy (EGaIn) enclosed in elastomeric microfluidic channels. Polydimethylsiloxane (PDMS) material is used as a supporting substrate. The proposed MM absorber is flexible because of its liquid metal and PDMS substrate. Numerical simulations and experimental results are presented when the microfluidic channels are filled with liquid metal. In order to evaluate the proposed MM absorber's performance, the fabricated absorber prototype is tested with rectangular waveguides. Almost perfect absorptivity is achieved at a resonant frequency of 8.22 GHz.