This work includes a comprehensive analysis of the Kepler detached eclipsing binary system KIC 6629588 that aims at the detailed study of the oscillation properties of its pulsating component. Ground-based spectroscopic observations were obtained and used to classify the components of the system. The spectroscopic results were used as constraints for the modeling of the short-cadence Kepler light curves and for the estimation of the absolute parameters of the components. Furthermore, the light curve residuals are analyzed using Fourier transformation techniques in order to search for pulsation frequencies. The primary component of the system is identified as a delta Sct star that pulsates in seven eigenfrequencies in the range of 13-22d^-1^, while more than 270 combination frequencies were also detected. The absolute and the oscillation parameters of this pulsating star are compared with those of other d Sct stars, members of detached binary systems, using evolutionary and correlation diagrams. Finally, the distance to the system is also estimated.