GaN/AlN heterostructures with thicknesses of one monolayer (ML) are currently considered to be the most promising material for creating UVC light-emitting devices. A unique functional property of these atomically thin quantum wells (QWs) is their ability to maintain stable excitons, resulting in a particularly high radiation yield at room temperature. However, the intrinsic properties of these excitons are substantially masked by the inhomogeneous broadening caused, in particular, by fluctuations in the QWs’ thicknesses. In this work, to reduce this effect, we fabricated cylindrical nanocolumns of 50 to 5000 nm in diameter using GaN/AlN single QW heterostructures grown via molecular beam epitaxy while using photolithography with a combination of wet and reactive ion etching. Photoluminescence measurements in an ultrasmall QW region enclosed in a nanocolumn revealed that narrow lines of individual excitons were localized on potential fluctuations attributed to 2-3-monolayer-high GaN clusters, which appear in QWs with an average thickness of 1 ML. The kinetics of luminescence with increasing temperature is determined via the change in the population of localized exciton states. At low temperatures, spin-forbidden dark excitons with lifetimes of ~40 ns predominate, while at temperatures elevated above 120 K, the overlying bright exciton states with much faster recombination dynamics determine the emission.