KIC 10661783 is an eclipsing binary that shows delta Sct-like oscillations. More than 60 pulsation frequencies have been detected in its light curve as observed by the Kepler satellite. We want to determine the fundamental stellar and system parameters of the eclipsing binary as a precondition for asteroseismic modelling of the pulsating component and to establish whether the star is a semi-detached Algol-type system. We measured the radial velocities of both components from new high-resolution spectra using TODCOR and compute the orbit using PHOEBE. We used the KOREL program to decompose the observed spectra into its components, and analysed the decomposed spectra to determine the atmospheric parameters. For this, we developed a new computer program for the normalisation of the KOREL output spectra. Fundamental stellar parameters are determined by combining the spectroscopic results with those from the analysis of the Kepler light curve. We obtain Teff, logg, vsini, and the absolute masses and radii of the components, together with their flux ratio and separation. Whereas the secondary star rotates synchronously with the orbital motion, the primary star rotates subsynchronously by a factor of 0.75. The newly determined mass ratio of 0.0911 is higher than previously thought and means a detached configuration is required to fit the light curve. With its low orbital period and very low mass ratio, the system shows characteristics of the R CMa-type stars but differs from this group by being detached. Its current state is assumed to be that of a detached post-Algol binary system with a pulsating primary component.