In recent years, Green Chemistry methods have been intensively developed to reduce the harmful effects of chemical processes on the environment. Dimethyl carbonate is an effective substitute for toxic methyl halides and phosgene. We have developed for the first time a new catalytic method for the preparation of arylmethyl ethers based on the reaction of phenol and its derivatives, as well as α- and β-naphthols with dimethyl carbonate in the presence of FeHYmmm zeolite of a hierarchical micro-, meso- and macroporous structure with a high degree of crystallinity. The optimal molar catalyst and reagents, as well as the reaction conditions for the selective synthesis of arylmethyl ethers, have been found. The nature and position of the substituent in the phenol molecule do not significantly affect the selectivity of the reaction, but affect the yield of esters. The presence of meso- and macropores in the catalyst creates conditions for effective diffusion of reactant molecules to catalytically active sites.