The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basic idea of MSLP is to construct low-rank approximations of the network at multiple scales in an efficient manner. To achieve this, we propose a fast tree-structured approximation algorithm. Based on this approach, MSLP combines predictions at multiple scales to make robust and accurate predictions. Experimental results on real-life datasets with more than a million nodes show the superior performance and scalability of our method.