Context : Aims : To probe the circumstellar environment of IRAS 13481-6124 , a 20 M _ { \sun } high-mass young stellar object ( HMYSO ) with a collimated parsec-scale jet and an accretion disc , we investigate the origin of its Br \gamma emission line through NIR interferometry . Methods : We present the first AMBER/VLTI observations of the Br \gamma emitting region in an HMYSO at medium spectral resolution ( \mathrm { R } =1500 ) . Results : Our AMBER/VLTI observations reveal a spatially and spectrally resolved Br \gamma line in emission with a strong P Cygni profile , indicating outflowing matter with a terminal velocity of \sim 500 km s ^ { -1 } . Visibilities , differential phases , and closure phases are detected in our observations within the spectral line and in the adjacent continuum . Both total visibilities ( continuum plus line emitting region ) and pure-line visibilities indicate that the Br \gamma -emitting region is more compact ( 2–4 mas in diameter or \sim 6–13 au at 3.2 kpc ) than the continuum-emitting region ( \sim 5.4 mas or \sim 17 au ) . The absorption feature is also spatially resolved at the longest baselines ( 81 and 85 m ) and has a visibility that is slightly smaller than the continuum-emitting region . The differential phases at the four longest baselines display an ‘ S ’ -shaped structure across the line , peaking in the blue- and red-shifted high-velocity components . The calibrated photocentre shifts are aligned with the known jet axis , i.e they are probably tracing an ionised jet . The high-velocity components ( v _ { r } \sim 100–500 km s ^ { -1 } ) are located far from the source , whereas the low-velocity components ( 0–100 km s ^ { -1 } ) are observed to be closer , indicating a strong acceleration of the gas flow in the inner 10 au . Finally , a non-zero closure phase along the continuum is detected . By comparing our observations with the synthetic images of the continuum around 2.16 \mu m , we confirm that this feature originates from the asymmetric brightness distribution of the continuum owing to the inclination of the inner disc . Conclusions :