Hi-C sequencing technology provides key insights into the 3D structures of the human genome. Although peak detection from Hi-C experiments is a well-studied problem, quantitative comparison of Hi-C across different cellular conditions largely depends on methods borrowed from RNA-seq data analysis. Such comparisons have critical shortcomings involving testing a large collection of hypotheses in large-scale Hi-C studies. As a result, these existing strategies for detecting differential interactions fail to control the rate of false discovery (FDR) for reported findings in many simulations and experimental Hi-C studies, hindering their comparative analysis. To address these issues, we present TreeHiC, the first hierarchical multiple testing procedure for quantitative comparison applied to Hi-C data. We demonstrate that this framework can detect differential interactions while assuring control of the FDR in complex large-scale Hi-C studies under a wide range of settings. It also is considerably more powerful than existing methods, especially in sparse testing problems where number of hypotheses could be millions with a weak signal-to-noise ratio. Additionally, while the current version of TreeHiC implements methodology pertaining to Hi-C differential analysis, it is easily extendable for other similar data such as ChIA-PET and HiChIP.