In this paper, we consider the challenge of face morphing attacks, which substantially undermine the integrity of face recognition systems such as those adopted for use in border protection agencies. Morph detection can be formulated as extracting fine-grained representations, where local discriminative features are harnessed for learning a hypothesis. To acquire discriminative features at different granularity as well as a decoupled spectral information, we leverage wavelet domain analysis to gain insight into the spatial-frequency content of a morphed face. As such, instead of using images in the RGB domain, we decompose every image into its wavelet sub-bands using 2D wavelet decomposition and a deep supervised feature selection scheme is employed to find the most discriminative wavelet sub-bands of input images. To this end, we train a Deep Neural Network (DNN) morph detector using the decomposed wavelet sub-bands of the morphed and bona fide images. In the training phase, our structured group sparsity-constrained DNN picks the most discriminative wavelet sub-bands out of all the sub-bands, with which we retrain our DNN, resulting in a precise detection of morphed images when inference is achieved on a probe image. The efficacy of our deep morph detector which is enhanced by structured group lasso is validated through experiments on three facial morph image databases, i.e., VISAPP17, LMA, and MorGAN.