Context: MWC 297 is a nearby young massive B[e] star. The central star is attenuated by 8 mag in the optical and has a high projected rotational velocity of 350 km s-1. Despite the wealth of published observations, the nature of this object and its circumstellar environment is not understood very well. Aims: With the present paper, we intend to shed light on the geometrical structure of the circumstellar matter that is responsible for the near- to mid-infrared flux excess. Methods: The H-band (1.6-2.0 μm), K-band (2.0-2.5 μm), and N-band (8-13 μm) brightness distribution of MWC 297 was probed with the ESO interferometric spectrographs AMBER and MIDI, mounted on the VLTI in Paranal, Chile. We obtained visibility measurements on 3 AMBER and 12 MIDI baselines, covering a wide range of spatial frequencies. Different models (parametrized circumstellar disks, a dusty halo) were invoked to fit the data, all of which fail to do so in a satisfying way. We approximated the brightness distribution in H, K, and N with a geometric model consisting of three Gaussian disks with different extents and brightness temperatures. This model can account for the entire near- to mid-IR emission of MWC 297. Results: The circumstellar matter around MWC 297 is resolved on all baselines. The near- and mid-IR emission, including the silicate emission at 10 micron, emanates from a very compact region (FWHM < 1.5 AU) around the central star. Conclusions: We argue that the extinction towards the MWC 297 star+disk system is interstellar and most likely due to remnants of the natal cloud from which MWC 297 was formed. Furthermore, we argue that the circumstellar matter in the MWC 297 system is organized in a circumstellar disk, seen under moderate (i < 40°) inclination. The disk displays no inner emission-free gap at the resolution of our interferometric observations. The low inclination of the disk implies that the already high projected rotational velocity of the star corresponds to an actual rotational velocity that exceeds the critical velocity of the star. This result shows that stars can obtain such high rotation rates at birth. We discuss the impact of this result in terms of the formation of high-mass stars and the main-sequence evolution of classical Be stars.