Obstructive Sleep Apnea (OSA) is one of the main under-diagnosed sleep disorder. It is an aggravating factor for several serious cardiovascular diseases, including stroke. There is, however, a lack of medical devices for long-term ambulatory monitoring of OSA since current systems are rather bulky, expensive, intrusive, and cannot be used for long-term monitoring in ambulatory settings. In this paper, we propose a wearable, accurate, and energy efficient system for monitoring obstructive sleep apnea on a long-term basis. As an embedded system for Internet of Things (IoT), it reduces the gap between home health-care and professional supervision. Our approach is based on monitoring the patient using a single-channel electrocardiogram (ECG) signal. We develop an efficient time-domain analysis to meet the stringent resources constraints of embedded systems to compute the sleep apnea score. Our system, for a publicly available database (PhysioNet Apnea-ECG), has a classification accuracy of up to 88.2% for our new online and patient-specific analysis, which takes the distinct profile of each patient into account. While accurate, our approach is also energy efficient and can achieve a battery lifetime of 46 days for continuous screening of OSA.