The use of an extrusion-spheronization process was investigated to prepare robust and highly porous extrudates and granules starting from UiO-66 and UiO-66_NH2 metal–organic framework powders. As-produced materials were applied to the capture of gaseous iodine and the adsorption of xenon and krypton. In this study, biosourced chitosan and hydroxyethyl cellulose (HEC) are used as binders, added in low amounts (less than 5 wt % of the dried solids), as well as a colloidal silica as a co-binder when required. Characterizations of the final shaped materials reveal that most physicochemical properties are retained, except the textural properties, which are impacted by the process and the proportion of binders (BET surface area reduction from 5 to 33%). On the other hand, the mechanical resistance of the shaped materials toward compression is greatly improved by the presence of binders and their respective contents, from 0.5 N for binderless UiO-66 granules to 17 N for UiO-66@HEC granules. UiO-66_NH2-based granules demonstrated consequent iodine capture after 48 h, up to 527 mg/g, in line with the pristine UiO-66_NH2 powder (565 mg/g) and proportionally to the retaining BET surface area (−5% after shaping). Analogously, the shaped materials presented xenon and krypton sorption isotherms correlated to their BET surface area and high predicted xenon/krypton selectivity, from 7.1 to 9.0. Therefore, binder-aided extrusion-spheronization is an adapted method to produce shaped solids with adequate mechanical resistance and retained functional properties.