Computerized brain tumor classification from the reconstructed microwave brain (RMB) images is important for the examination and observation of the development of brain disease. In this paper, an eight-layered lightweight classifier model called microwave brain image network (MBINet) using a self-organized operational neural network (Self-ONN) is proposed to classify the reconstructed microwave brain (RMB) images into six classes. Initially, an experimental antenna sensor-based microwave brain imaging (SMBI) system was implemented, and RMB images were collected to create an image dataset. It consists of a total of 1320 images: 300 images for the non-tumor, 215 images for each single malignant and benign tumor, 200 images for each double benign tumor and double malignant tumor, and 190 images for the single benign and single malignant tumor classes. Then, image resizing and normalization techniques were used for image preprocessing. Thereafter, augmentation techniques were applied to the dataset to make 13,200 training images per fold for 5-fold cross-validation. The MBINet model was trained and achieved accuracy, precision, recall, F1-score, and specificity of 96.97%, 96.93%, 96.85%, 96.83%, and 97.95%, respectively, for six-class classification using original RMB images. The MBINet model was compared with four Self-ONNs, two vanilla CNNs, ResNet50, ResNet101, and DenseNet201 pre-trained models, and showed better classification outcomes (almost 98%). Therefore, the MBINet model can be used for reliably classifying the tumor(s) using RMB images in the SMBI system.