HKUST-1 is an MOF adsorbent industrially produced in powder form and thus requires a post-shaping process for use as an adsorbent in fixed-bed separation processes. HKUST-1 is also sensitive to moisture, which degrades its crystalline structure. In this work, HKUST-1, in the form of crystalline powder, was extruded into pellets using a hydrophobic polymeric binder to improve its moisture stability. Thermoplastic polyurethane (TPU) was used for that purpose. The subsequent HKUST-1/TPU extrudate was then compared to HKUST-1/PLA extrudates synthesized with more hydrophilic polymer: polylactic acid (PLA), as the binder. The characterization of the composites was determined via XRD, TGA, SEM-EDS, and an N2 adsorption isotherm analysis. Meanwhile, the gas-separation performances of HKUST-1/TPU were investigated and compared with HKUST-1/PLA from measurements of CO2 and CH4 isotherms at three different temperatures, up to 10 bars. Lastly, the moisture stability of the composite materials was investigated via an aging analysis during storage under humid conditions. It is shown that HKUST-1's crystalline structure was preserved in the HKUST-1/TPU extrudates. The composites also exhibited good thermal stability under 523 K, whilst their textural properties were not significantly modified compared with the pristine HKUST-1. Furthermore, both extrudates exhibited larger CO2 and CH4 adsorption capacities in comparison to the pristine HKUST-1. After three months of storage under atmospheric humid conditions, CO2 adsorption capacities were reduced to only 10 for HKUST-1/TPU, whereas reductions of about 25 and 54 were observed for HKUST-1/PLA and the pristine HKUST-1, respectively. This study demonstrates the interest in shaping MOF powders by extrusion using a hydrophobic thermoplastic binder to operate adsorbents with enhanced moisture stability in gas-separation columns.