Integrated mid-infrared micro-spectrometers have a great potential for applications in environmental monitoring and space exploration. Silicon-on-insulator (SOI) is a promising platform to tackle this integration challenge, owing to its unique capability for large volume and low-cost production of ultra-compact photonic circuits. However, the use of SOI in the mid-infrared is restricted by the strong absorption of the buried oxide layer for wavelengths beyond 4 µm. Here, we overcome this limitation by utilizing metamaterial-cladded suspended silicon waveguides to implement a spatial heterodyne Fourier-transform (SHFT) spectrometer operating at wavelengths near 5.5 µm. The metamaterial-cladded geometry allows removal of the buried oxide layer, yielding measured propagation loss below 2 dB/cm at wavelengths between 5.3 and 5.7 µm. The SHFT spectrometer comprises 19 Mach-Zehnder interferometers with a maximum arm length imbalance of 200 µm, achieving a measured spectral resolution of 13 cm-1 and a free spectral range of 100 cm-1 at wavelengths near 5.5 µm.