Context. Herschel observations of nearby molecular clouds suggest that interstellar filaments and prestellar cores represent two fundamental steps in the star formation process. The observations support a picture of low-mass star formation according to which filaments of ∼0.1 pc width form first in the cold interstellar medium, probably as a result of large-scale compression of interstellar matter by supersonic turbulent flows, and then prestellar cores arise from gravitational fragmentation of the densest filaments. Whether this scenario also applies to regions of high-mass star formation is an open question, in part because the resolution of Herschel is insufficient to resolve the inner width of filaments in the nearest regions of massive star formation. Aims. In an effort to characterize the inner width of filaments in high-mass star-forming regions, we imaged the central part of the NGC 6334 complex at a resolution higher by a factor of >3 than Herschel at 350 µm. Methods. We used the large-format bolometer camera ArTéMiS on the APEX telescope and combined the high-resolution ArTéMiS data at 350 µm with Herschel/HOBYS data at 70-500 µm to ensure good sensitivity to a broad range of spatial scales. This allowed us to study the structure of the main narrow filament of the complex with a resolution of 8 or <0.07 pc at d ∼ 1.7 kpc. Results. Our study confirms that this filament is a very dense, massive linear structure with a line mass ranging from ∼500 M /pc to ∼2000 M /pc over nearly 10 pc. It also demonstrates for the first time that its inner width remains as narrow as W ∼ 0.15 ± 0.05 pc all along the filament length, within a factor of <2 of the characteristic 0.1 pc value found with Herschel for lower-mass filaments in the Gould Belt. Conclusions. While it is not completely clear whether the NGC 6334 filament will form massive stars in the future, it is two to three orders of magnitude denser than the majority of filaments observed in Gould Belt clouds, and has a very similar inner width. This points to a common physical mechanism for setting the filament width and suggests that some important structural properties of nearby clouds also hold in high-mass star-forming regions.Key words. stars: formation -circumstellar matter -ISM: clouds -ISM: structure -ISM: individual objects: NGC 6334 -submillimeter: ISM This publication is based on data acquired with the Atacama Pathfinder Experiment (APEX) in ESO program 091.C-0870. APEX is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory.The final ArTéMiS+SPIRE 350 µm map (Fig. 1b) is available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via