In millimeter-wave communications, multiple-input-multiple-output (MIMO) systems use large antenna arrays to achieve high gain and spectral efficiency. These massive MIMO systems employ hybrid beamformers to reduce power consumption associated with fully digital beamforming in large arrays. Further savings in cost and power are possible through the use of subarrays. Unlike prior works that resort to large latency methods such as optimization and greedy search for subarray selection, we propose a deep-learning-based approach in order to overcome the complexity issue without causing significant performance loss. We formulate antenna selection and hybrid beamformer design as a classification/prediction problem for convolutional neural networks (CNNs). For antenna selection, the CNN accepts the channel matrix as input and outputs a subarray with optimal spectral efficiency. The resultant subarray channel matrix is then again fed to a CNN to obtain analog and baseband beamformers. We train the CNNs with several noisy channel matrices that have different channel statistics in order to achieve a robust performance at the network output. Numerical experiments show that our CNN framework provides an order better spectral efficiency and is 10 times faster than the conventional techniques. Further investigations with quantized-CNNs show that the proposed network, saved in no more than 5 bits, is also suited for digital mobile devices.