The origin of the Br γ line in Herbig Ae/Be stars is still an open question. It has been proposed that a fraction of the 2.166-μm Br γ emission might emerge from a disc wind, the magnetosphere and other regions. Investigations of the Br γ line in young stellar objects are important to improve our understanding of the accretion-ejection process. Near-infrared longbaseline interferometry enables the investigation of the Br γ line-emitting region with high spatial and high spectral resolution. We observed the Herbig Ae/Be star MWC 120 with the Astronomical Multi-Beam Recombiner (AMBER) on theVery Large Telescope Interferometer (VLTI) in different spectral channels across the Br γ linewith a spectral resolution of R~1500. Comparison of the visibilities, differential and closure phases in the continuum and the lineemitting region with geometric and radiative transfer disc-wind models leads to constraints on the origin and dynamics of the gas emitting the Br γ light. Geometric modelling of the visibilities reveals a line-emission region about two times smaller than the K-band continuum region, which indicates a scenario where the Br γ emission is dominated by an extended disc wind rather than by a much more compact magnetospheric origin. To compare our data with a physical model, we applied a state-of-the-art radiative transfer disc-wind model. We find that all measured visibilities, differential and closure phases of MWC 120 can be approximately reproduced by a disc-wind model. A comparison with other Herbig stars indicates a correlation of the modelled inner disc-wind radii with the corresponding Alfvén radii for late spectral type stars.