We propose a new method based on graph cuts for the segmentation of burned areas in time series of satellite images. The method consists in rewriting a segmentation problem as a (s, t)-min-cut on the spatio-temporal image graph and computing this minimal cut. As burned areas grow in time, we introduce growth constraint in graph cuts by using directed infinite links connecting pixels at the same spatial locations in successive image frames. This method guarantees to find the globally optimal segmentation satisfying the growth constraint in small time complexity. Experimental results on a set of MODIS measurements over the Northern Australia demonstrated that the new approach succeeded in combining both spatial and temporal information for accurate segmentation of burned areas.