Comparative analysis of available molecular interaction data reveals that various network components and properties are conserved across diverse species. These observations motivate phylogenetic analysis of extant molecular networks with a view to understanding the functional evolution of biological systems. However, application of existing comparative network analysis techniques to large scale phylogenetic network analysis is limited by various factors; including noisy and incomplete nature of interaction data, intractability of network comparison problems, lack of sound biological bases for formulating network similarity, and limited theoretical understanding of network evolution. In this paper, we propose a modularity-based framework for phylogenetic network analysis, with applications that extend well beyond network-based phylogeny reconstruction. Our approach is based on identification of modular network components from each species separately, followed by projection of these modules onto the networks of other species to compare different networks. This approach has key advantages in (i) avoiding intractable graph comparison problems, (ii) accounting for noise and missing data through flexible treatment of network conservation, and (iii) providing insights on the evolution of biological systems through investigation of the evolutionary trajectories of network modules. We test our method, Mophy, on synthetic data generated by simulation of network evolution based on detailed evolutionary models, as well as existing protein-protein interaction data for seven diverse species. Comprehensive experimental results show that Mophy is quite promising in network-based phylogenetic analysis, is highly robust to noise, and outperforms existing methods. These results establish modularity and network proximity as useful measures in comparative network analysis and motivate the study of the evolution of network modules. These authors have contributed equally to this article.