Obstructive sleep apnea (OSA) is a prevalent sleep disorder associated with anatomical abnormalities of the upper airway. It is known that anatomic changes in the vocal tract affect the acoustic parameters of speech. We hypothesize that the speech signal contains valuable information that can be utilized for the assessment of OSA severity. We prospectively included 131 men with a variety of OSA severities; subjects were recorded immediately prior to polysomnography study while reading a one-minute speech protocol. Features from time and spectra domains were extracted, and a feature selection procedure was applied. Using a support vector regression (SVR), the proposed system estimates OSA severity, which is defined by the apnea-hypopnea index (AHI: the average number of apneic events per hour of sleep). Correlation of R=0.67, AHI error of 10.17 events/hr, and diagnostic agreement of 66.7% were achieved. This study provides the proof of concept that it is possible to estimate OSA severity by analyzing speech signals.