ABSTRACT Alhena A (γ Gem A) is a bright Am star, with the strongest disc-integrated magnetic field strength reported so far for an Am star. Its spectrum exhibits standard circularly polarized Zeeman signatures, contrary to all previously studied Am stars that display abnormal signatures dominated by a single-signed lobe. We present here the result of follow-up observations of Alhena, using very high signal-to-noise spectropolarimetric data obtained over 25 observing nights with NARVAL at Télescope Bernard Lyot, in the frame of the BRITE (BRIght Target Explorer) spectropolarimetric survey. We confirm that Alhena A is magnetic and we determine its surface magnetic properties using different methods. Inclined dipole models are used to reproduce the longitudinal field measurements, as well as the Stokes V line profiles themselves. In both cases, the model is consistent with a polar field strength of ∼30 G. This is confirmed by a Zeeman-Doppler Imaging (ZDI) model, which also unveils smaller scale magnetic structures. A rotational period of 8.975 d was identified using intensity line profile variations. The ZDI inversion suggests that the surface magnetic field is sheared by differential rotation, with a difference in rotation rate between high and low latitudes at about 15 per cent of the solar value. This result challenges theories of the development of surface differential rotation in intermediate mass main-sequence stars.