Recent studies indicate that detecting radiographic patterns on CT chest scans can yield high sensitivity and specificity for COVID-19 identification. In this paper, we scrutinize the effectiveness of deep learning models for semantic segmentation of pneumonia-infected area segmentation in CT images for the detection of COVID-19. Traditional methods for CT scan segmentation exploit a supervised learning paradigm, so they (a) require large volumes of data for their training, and (b) assume fixed (static) network weights once the training procedure has been completed. Recently, to overcome these difficulties, few-shot learning (FSL) has been introduced as a general concept of network model training using a very small amount of samples. In this paper, we explore the efficacy of few-shot learning in U-Net architectures, allowing for a dynamic fine-tuning of the network weights as new few samples are being fed into the U-Net. Experimental results indicate improvement in the segmentation accuracy of identifying COVID-19 infected regions. In particular, using 4-fold cross-validation results of the different classifiers, we observed an improvement of 5.388 ± 3.046% for all test data regarding the IoU metric and a similar increment of 5.394 ± 3.015% for the F1 score. Moreover, the statistical significance of the improvement obtained using our proposed few-shot U-Net architecture compared with the traditional U-Net model was confirmed by applying the Kruskal-Wallis test (p-value = 0.026).