This paper studies the distributed change detection problem in Gaussian graphical models (GGMs). Statistical analysis in GGM leads to several advantages, including a smaller number of parameters to model a large scale distribution, less samples required for the detection, faster detection and less communication costs. We formulate the hypothesis testing problem for change detection in GGMs and propose a global and centralized solution using the generalized likelihood ratio test (GLRT). We then provide two distributed approximations to this global test based on aggregation of multiple local or conditional tests. We compare the performance of these tests in the context of failure detection in smart grids.