We show that smooth variations, δn(r), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, ν(ω), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, ω0, of the anomaly scales with the magnitude, δn, and characteristic spatial extent, D, of the fluctuations as (δn/D)2/3, while the relative magnitude δν/ν scales as (δn/D). With increasing ω, the averaged δν oscillates with ω. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairs.