We report the detection of the Doppler shadow of the transiting hot Jupiter CoRoT-11b. Our analysis is based on line-profile tomography of time-series, Keck/HIRES high-resolution spectra acquired during the transit of the planet. We measured a sky-projected, spin-orbit angle λ = 0.1° ± 2.6°, which is consistent with a very low-inclined orbit with respect to the stellar rotation axis. We refined the physical parameters of the system using a Markov chain Monte Carlo simultaneous fitting of the available photometric and spectroscopic data. An analysis of the tidal evolution of the system shows how the currently measured obliquity and its uncertainty translate into an initial absolute value of less than about 10° on the zero-age main sequence, for an expected average modified tidal quality factor of the star ⟨ Q '* ' ⟩ ≳ 4 × 106. This is indicative of an inward migration scenario that would not have perturbed the primordial low obliquity of CoRoT-11b. Taking into account the effective temperature and mass of the planet host star (Teff = 6440 K, M⋆ = 1.23 M&sun;), the system can be considered a new telling exception to the recently proposed trend, according to which relatively hot and massive stars (Teff > 6250 K, M⋆ > 1.2 M&sun;) seem to be preferentially orbited by hot Jupiters with high obliquity.