Eclipsing binaries in open clusters - III. V621 Per in χ Persei

V621 Persei is a detached eclipsing binary in the open cluster χ Persei, which is composed of an early B-type giant star and a main-sequence secondary component. From high-resolution spectroscopic observations and radial velocities from the literature, we determine the orbital period to be 25.5 d and the primary velocity semi-amplitude to be K= 64.5 +/- 0.4 km s^-1. No trace of the secondary star has been found in the spectrum. We solve the discovery light curves of this totally eclipsing binary and find that the surface gravity of the secondary star is logg_B= 4.244 +/- 0.054. We compare the absolute masses and radii of the two stars in the mass-radius diagram, for different possible values of the primary surface gravity, with the predictions of stellar models. We find that logg_A~ 3.55, in agreement with values found from fitting Balmer lines with synthetic profiles. The expected masses of the two stars are 12 and 6 M_solar and the expected radii are 10 and 3 R_solar. The primary component is near the blue loop stage in its evolution.