1. An apparatus for processing a magnetic resonance (MR) image, the apparatus comprising: an image acquisition unit configured to acquire a plurality of MR images by performing MR imaging on a moving object during temporally consecutive time intervals; a controller configured to sequentially compare two adjacent MR images from among the plurality of MR images to detect an interval during which motion occurs; an image processor configured to calculate a transformation matrix for performing motion correction on at least one MR image corresponding to the detected interval and obtain a motion-corrected MR image by applying the transformation matrix to the at least one MR image; and an output unit configured to display the motion-corrected MR image.