Context. Stellar evolution models are highly dependent on accurate mass estimates, especially for highly massive stars in the early stages of stellar evolution. The most direct method for obtaining model-independent stellar masses is derivation from the orbit of close binaries. Aims. Our aim was to derive the first astrometric plus radial velocity orbit solution for the single-lined spectroscopic binary star MWC 166 A, based on near-infrared interferometry over multiple epochs and ∼100 archival radial velocity measurements, and to derive fundamental stellar parameters from this orbit. A supplementary aim was to model the circumstellar activity in the system from K band spectral lines. Methods. The data used include interferometric observations from the VLTI instruments GRAVITY and PIONIER, as well as the MIRC-X instrument at the CHARA Array. We geometrically modelled the dust continuum to derive relative astrometry at 13 epochs, determine the orbital elements, and constrain individual stellar parameters at five different age estimates. We used the continuum models as a base to examine differential phases, visibilities, and closure phases over the Br γ and He I emission lines in order to characterise the nature of the circumstellar emission. Results. Our orbit solution suggests a period of P = 367.7 ± 0.1 d, approximately twice as long as found with previous radial velocity orbit fits. We derive a semi-major axis of 2.61 ± 0.04 au at d = 990 ± 50 pc, an eccentricity of 0.498 ± 0.001, and an orbital inclination of 53.6 ± 0.3°. This allowed the component masses to be constrained to M₁ = 12.2 ± 2.2 M_⊙ and M₂ = 4.9 ± 0.5 M_⊙. The line-emitting gas was found to be localised around the primary and is spatially resolved on scales of ∼11 stellar radii, where the spatial displacement between the line wings is consistent with a rotating disc. Conclusions. The large spatial extent and stable rotation axis orientation measured for the Br γ and He I line emission are inconsistent with an origin in magnetospheric accretion or boundary-layer accretion, but indicate an ionised inner gas disc around this Herbig Be star. We observe line variability that could be explained either with generic line variability in a Herbig star disc or V/R variations in a decretion disc scenario. We have also constrained the age of the system, with relative flux ratios suggesting an age of ∼(7 ± 2)×10⁵ yr, consistent with the system being composed of a main-sequence primary and a secondary still contracting towards the main-sequence stage.