The manufacturing of nanomaterials by an electrospinning process requires accurate and meticulous inspection of Scanning Electron Microscope (SEM) images of the electrospun nanofiber, to ensure no structural defects are produced. The possible presence of anomalies is known to make the nanofibrous material useless in the practical application of any nanotechnology. Hence, automatic monitoring and quality control of nanomaterials has become an important challenge in the context of Industry 4.0. In this paper, we propose a novel automatic classification system for homogenous (anomaly-free) and nonhomogenous (with defects) nanofibers avoiding the processing of the redundant full SEM image. Specifically, the image to be analyzed is partitioned into sub-images (nanopatches) that are then used as input to a hybrid unsupervised and supervised machine learning system. An Autoencoder (AE) is first trained with unsupervised learning to generate a code representing the input image with a number of relevant features. Next, a Multilayer Perceptron (MLP), trained with supervised learning, uses the extracted features to classify non-homogenous nanofiber (NH-NF) and homogenous nanofiber (H-NF) materials. The resulting novel AE-MLP system is shown to outperform other standard machine learning models and recent state-of-the-art techniques, reporting accuracy rates up to 92.5%. In addition, our proposed approach achieves significant model complexity reduction with respect to other deep learning strategies such as Convolutional Neural Networks (CNN). The promising performance achieved in this benchmark study will stimulate the application of our proposed framework in a range of challenging industrial manufacturing tasks.