Face recognition systems are extremely vulnerable to morphing attacks, in which a morphed facial reference image can be successfully verified as two or more distinct identities. In this paper, we propose a morph attack detection algorithm that leverages an undecimated 2D Discrete Wavelet Transform (DWT) for identifying morphed face images. The core of our framework is that artifacts resulting from the morphing process that are not discernible in the image domain can be more easily identified in the spatial frequency domain. A discriminative wavelet sub-band can accentuate the disparity between a real and a morphed image. To this end, multi-level DWT is applied to all images, yielding 48 mid and high-frequency sub-bands each. The entropy distributions for each sub-band are calculated separately for both bona fide and morph images. For some of the sub-bands, there is a marked difference between the entropy of the sub-band in a bona fide image and the identical sub-band's entropy in a morphed image. Consequently, we employ Kullback-Liebler Divergence (KLD) to exploit these differences and isolate the sub-bands that are the most discriminative. We measure how discriminative a sub-band is by its KLD value and the 22 sub-bands with the highest KLD values are chosen for network training. Then, we train a deep Siamese neural network using these 22 selected sub-bands for differential morph attack detection. We examine the efficacy of discriminative wavelet sub-bands for morph attack detection and show that a deep neural network trained on these sub-bands can accurately identify morph imagery.