Microwave permeability of glass-coated ferromagnetic amorphous microwire exhibiting a weak negative magnetostriction has been studied. The diameter of the microwire was about 20 m and the diameter of the metal core was about 12 m. The microwire was wound to comprise a 7/3 washer-shaped composite sample with the volume fraction of magnetic constituent of about 10%. The permeability of the composite sample was measured in a coaxial line in the frequency range from 0.1 to 10 GHz. The composite was found to exhibit a negative permeability within the frequency range from approximately 0.7 to 1.5 GHz, with the permeability being as low as −0.4. Therefore, microwire-based composites, particularly, crossed arrays of microwires may be employed to develop metamaterials for microwave applications. In the composite, the negative microwave permeability is due to the natural ferromagnetic resonance and the negative microwave permittivity is due to the inherent inductance of the wire. Such metamaterials are advantageous in simple design, isotropic in-plane performance, and possible tunability of performance by external magnetic bias. However, for a feasible metamaterial fabricated from microwire arrays, the wires have to exhibit higher magnitude of the ferromagnetic resonance, higher quality factor, and higher resonance frequency.