Spectral features from polycyclic aromatic hydrocarbon (PAH) molecules observed in the mid-infrared (mid-IR) range are typically used to infer the amount of recent and ongoing star formation on kiloparsec scales around active galactic nuclei (AGN) where more traditional methods fail. This method assumes that the observed PAH features are excited predominantly by star formation. With current ground-based telescopes and the upcoming James Webb Space Telescope, much smaller spatial scales can be probed and we aim at testing if this assumption still holds in the range of few tens to few hundreds of parsecs. For that, we spatially map the emitted 11.3um PAH surface flux as a function of distance from 0.4-4 arcsec from the centre in 28 nearby AGN using ground-based high-angular-resolution mid-IR spectroscopy. We detect and extract the 11.3um PAH feature in 13 AGN. The fluxes within each aperture are scaled to a luminosity-normalized distance from the nucleus to be able to compare intrinsic spatial scales of AGN radiation spanning about two orders of magnitude in luminosity. For this, we establish an empirical relation between the absorption-corrected X-ray luminosity and the sublimation radius in these sources. Once normalized, the radial profiles of the emitted PAH surface flux show similar radial slopes, with a power-law index of approximately -1.1, and similar absolute values, consistent within a factor of a few of each other as expected from the uncertainty in the intrinsic scale estimate. We interpret this as evidence that the profiles are caused by a common compact central physical process, either the AGN itself or circumnuclear star formation linked in strength to the AGN power. A photoionization-based model of an AGN exciting dense clouds in its environment can reproduce the observed radial slope and confirms that the AGN radiation field is strong enough to explain the observed PAH surface fluxes within ~10-500pc of the nucleus. Our results advice caution in the use of PAH emission as a star formation tracer within a kpc around AGN.