Characterization of the dynamics of massive star systems and the astrophysical properties of the interacting components are a prerequisite for understanding their formation and evolution. Optical interferometry at milliarcsecond resolution is a key observing technique for resolving high-mass multiple compact systems. Here, we report on Very Large Telescope Interferometer/GRAVITY, Magellan/Folded-port InfraRed Echellette, and MPG2.2 m/FEROS observations of the late-O/early-B type system HD 93206 A, which is a member of the massive cluster Collinder 228 in the Carina nebula complex. With a total mass of about 90 M-circle dot, it is one of the most compact massive quadruple systems known. In addition to measuring the separation and position angle of the outer binary Aa-Ac, we observe Br gamma and He I variability in phase with the orbital motion of the two inner binaries. From the differential phase (Delta(phi)) analysis, we conclude that the Br gamma emission arises from the interaction regions within the components of the individual binaries, which is consistent with previous models for the X-ray emission of the system based on wind-wind interaction. With an average 3 sigma deviation of Delta(phi) similar to 15 degrees, we establish an upper limit of p similar to 0.157 mas ( 0.35 au) for the size of the Br gamma line-emitting region. Future interferometric observations with GRAVITY using the 8 m Unit Telescopes will allow us to constrain the line-emitting regions down to angular sizes of 20 mu as (0.05 au at the distance of the Carina nebula).