Obstructive sleep apnea (OSA) is a severe sleep-associated respiratory disorder, caused due to periodic disruption of breath during sleep. It may cause a number of serious cardiovascular complications, including stroke. Generally, OSA is detected by polysomnography (PSG), a costly procedure, and may cause discomfort to the patient. Nowadays, electrocardiogram (ECG) signal-based detection techniques have been explored as an alternative to PSG for OSA detection. Usual linear and nonlinear machine learning techniques are mainly focused on handcrafted feature extraction and classification that are time-consuming and may not be suitable for huge data. Therefore, in this work, a deep learning model (DLM) using smoothed Gabor spectrogram (SGS) of ECG signals is proposed for automated OSA detection to obtain high performance. The proposed framework fed Gabor spectrogram and SGS of ECG signals as input to the pretrained Squeeze-Net, Res-Net50, and developed DLM called obstructive sleep apnea convolutional neural network (OSACN-Net). The proposed OSACN-Net achieved an average classification accuracy of 94.81% with SGS using a tenfold cross-validation strategy. Compared to Squeeze-Net and Res-Net50, developed OSACN-Net is more accurate and lightweight as it requires few learnable parameters, which makes it computationally fast and efficient. The comparison results showed that the proposed framework outperformed all existing state-of-the-art methodologies.