Obstructive sleep apnea (OSA) is a prevalent sleep disorder and highly affects the quality of human life. Currently, gold standard for OSA detection is polysomnogram. Since this method is time consuming and cost inefficient, practical systems focus on the usage of electrocardiogram (ECG) signals for OSA detection. In this paper, a novel automatic OSA detection method using a single-lead ECG signal has been proposed. A nonlinear feature extraction using wavelet transform (WT) coefficients obtained by an ECG signal decomposition is employed. In addition, different classification methods are investigated. ECG signals are decomposed into eight levels using a Symlet function as a mother Wavelet function with third order. Then, the entropy-based features including fuzzy/approximate/sample/correct conditional entropy as well as other nonlinear features including interquartile range, mean absolute deviation, variance, Poincare plot, and recurrence plot are extracted from WT coefficients. The best features are chosen using the automatic sequential forward feature selection algorithm. In order to assess the introduced method, 95 single-lead ECG recordings are used. The support vector machine classifier having a radial basis function kernel leads to an accuracy of 94.63% (sensitivity: 94.43% and specificity: 94.77%) and 95.71% (sensitivity: 95.83% and specificity: 95.66%) for minute-by-minute and subject-by-subject classifications, respectively. The results show that applying entropy-based features for extracting hidden information of the ECG signals outperforms other available automatic OSA detection methods. The results indicate that a highly accurate OSA detection is attained by just exploiting the single-lead ECG signals. Furthermore, due to the low computational load in the proposed method, it can easily be applied to the home monitoring systems.