Nanoparticles made of metal-organic frameworks (nanoMOFs) are becoming of increasing interest as drug carriers. However, preventing nanoMOFs recognition and clearance by the innate immune system, a prerequisite for biomedical applications, presents an important challenge. In this study we provide a proof of concept that the outer surface of biocompatible iron-based nanoMOFs can be functionalized in a rapid, organic solvent-free and non-covalent manner using a novel family of comb-like copolymers made of dextran (DEX) grafted with both poly(ethylene glycol) (PEG) and alendronate (ALN) moieties. We describe the synthesis and full characterization of DEX-PEG-ALN copolymers by click chemistry, with control of both the amount of grafted PEG and ALN moieties. The copolymers, freely soluble in aqueous media, were used to directly coat the nanoMOFs in water by simple incubation at room temperature. The coating procedure did not affect the nanoMOFs' morphology nor their crystalline structure. As strong iron complexing groups, the ALN moieties ensured multiple cooperative anchoring of the copolymers to the nanoMOFs surface, resulting in stable coatings that substantially decreased their internalization by macrophages in vitro, providing new perspectives for biomedical applications.