Application of machine learning (ML) algorithms to spectroscopic data has a great potential for obtaining hidden correlations between structural information and spectral features. Here, we apply ML algorithms to theoretically simulated infrared (IR) spectra to establish the structure-spectrum correlations in zeolites. Two hundred thirty different types of zeolite frameworks were considered in the study whose theoretical IR spectra were used as the training ML set. A classification problem was solved to predict the presence or absence of possible tilings and secondary building units (SBUs). Several natural tilings and SBUs were also predicted with an accuracy above 89%. The set of continuous descriptors was also suggested, and the regression problem was also solved using the ExtraTrees algorithm. For the latter problem, additional IR spectra were computed for the structures with artificially modified cell parameters, expanding the database to 470 different spectra of zeolites. The resulting prediction quality above or close to 90% was obtained for the average Si-O distances, Si-O-Si angles, and volume of TO4 tetrahedra. The obtained results provide new possibilities for utilization of infrared spectra as a quantitative tool for characterization of zeolites.