Obstructive sleep apnea (OSA) is a kind of sleep disorder and it is described by breathing irregularity during sleep. This disorder may lead to long-term consequences, such as sleep related irregularities and/or cardiovascular diseases. This paper proposes a multimodal and feature selection-based processing pipeline to detect OSA as a computerbased alternative way to clinical polysomnography (PSG) method. In the proposed method, the oxygen saturation (SpO2) and the electrocardiogram (ECG) signals are fused at the feature-level for the classification. Five feature selection methods, namely Relieff, Chi-Square, Information Gain (IG), Principal Component Analysis (PCA), and Gain Ratio (GR) were applied to the problem to obtain robust features from both signal sources and to reduce the feature dimensionality. The effectiveness of utilized feature selection methods was analyzed using the Support Vector Machine (SVM), k-nearest neighbor (k-NN), and Naive Bayes (NB) classifiers. The experimental results on the real clinical samples from the PhysioNet dataset show that the proposed multimodal and feature selection-based method improves the classification accuracy, significantly.