In this study, we use the overnight blood oxygen saturation (SpO2) signal along with convolutional neural networks (CNN) for the automatic estimation of pediatric sleep apnea-hypopnea syndrome (SAHS) severity. The few preceding studies have focused on the application of conventional feature extraction methods to obtain information from the SpO2 signal, which may omit relevant data related to the illness. In contrast, deep learning techniques are able to automatically learn features from raw input signal. Thus, we propose to assess whether CNN, a deep learning algorithm, could automatically estimate the apnea-hypopnea index (AHÍ) from nocturnal oximetry to help establish pediatric SAHS presence and severity. A database of 746 SpO2 recordings is involved in the study. CNN was trained using 20-min segments from the SpO2 signal in the training set (400 subjects). Hyperparameters of the CNN architecture were tuned using a validation set (100 subjects). This model was applied to a test set (246 subjects), in which the final AHI of each patient was obtained as the average of the output of the CNN for all the segments of the corresponding SpO2 signal. The AHI estimated by the CNN showed a promising diagnostic performance, with 74.8%, 90.7%, and 95.1% accuracies for the common AHI severity thresholds of 1, 5, and 10 events per hour (e/h), respectively. Furthermore, this model reached 28.6, 32.9, and 120.0 positive likelihood ratios for the above-mentioned AHI thresholds. This suggests that the information extracted from the oximetry signal by deep learning techniques may be useful to both establish pediatric SAHS and its severity.