A novel self-supervised deep learning (DL) method is developed to compute personalized brain functional networks (FNs) for characterizing brain functional neuroanatomy based on functional MRI (fMRI). Specifically, a DL model of convolutional neural networks with an encoder-decoder architecture is developed to compute personalized FNs directly from fMRI data. The DL model is trained to optimize functional homogeneity of personalized FNs without utilizing any external supervision in an end-to-end fashion. We demonstrate that a DL model trained on fMRI scans from the Human Connectome Project can identify personalized FNs and generalizes well across four different datasets. We further demonstrate that the identified personalized FNs are informative for predicting individual differences in behavior, brain development, and schizophrenia status. Taken together, the self-supervised DL allows for rapid, generalizable computation of personalized FNs.