We present near-infrared interferometric AMBER observations of the B[e] binary V921 Sco at low (R ~ 30) and medium spectral resolution (R ~ 1500) in the K and H bands. Low spectral resolution AMBER data were used to estimate the position of the companion V921 Sco B and confirmed a clockwise movement on sky with respect to the primary of 33? between 2008 and 2012. Our observations resolve for the first time higher order Brackett lines (Br6-Br12). The modelling of the different line transitions revealed a decrease in the size of the line-emitting regions from Br3 to Br12. We are able to reproduce this decrease with a simple radiative transfer model of an equatorial disc in local thermodynamic equilibrium. In addition to the Brackett series, we also resolve permitted and forbidden Fe line emission. Our modelling shows that these lines originate from ~2 au from the star, corresponding roughly to the measured dust sublimation region. This might indicate that the forbidden line emission arises from shock excitation at the base of a disc wind.