In the face of the COVID-19 pandemic, the World Health Organization (WHO) declared the use of a face mask as a mandatory biosafety measure. This has caused problems in current facial recognition systems, motivating the development of this research. This manuscript describes the development of a system for recognizing people, even when they are using a face mask, from photographs. A classification model based on the MobileNetV2 architecture and the OpenCv’s face detector is used. Thus, using these stages, it can be identified where the face is and it can be determined whether or not it is wearing a face mask. The FaceNet model is used as a feature extractor and a feedforward multilayer perceptron to perform facial recognition. For training the facial recognition models, a set of observations made up of 13,359 images is generated; 52.9% images with a face mask and 47.1% images without a face mask. The experimental results show that there is an accuracy of 99.65% in determining whether a person is wearing a mask or not. An accuracy of 99.52% is achieved in the facial recognition of 10 people with masks, while for facial recognition without masks, an accuracy of 99.96% is obtained.