The development of statistical tools based on machine learning (ML) and deep networks is actively sought for materials design problems. While structure-property relationships can be accurately determined using quantum mechanical methods, these first-principles calculations are computationally demanding, limiting their use in screening a large set of candidate structures. Herein, we use convolutional neural networks to develop a predictive model for the electronic properties of metal halide perovskites (MHPs) that have a billions-range materials design space. We show that a well-designed hierarchical ML approach has a higher fidelity in predicting properties of the MHPs compared to straight-forward methods. In this architecture, each neural network element has a designated role in the estimation process from predicting complex features of the perovskites such as lattice constant and octahedral till angle to narrowing down possible ranges for the values of interest. Using the hierarchical ML scheme, the obtained root-mean-square errors for the lattice constants, octahedral angle and bandgap for the MHPs are 0.01 angstrom, 5 degrees, and 0.02 eV, respectively. Our study underscores the importance of a careful network design and a hierarchical approach to alleviate issues associated with imbalanced dataset distributions, which is invariably common in materials datasets.