The quantum Smoluchowski equation is an equation for the coordinate-diagonal elements of the density operator, and it is identical to the classical Smoluchowski equation. Here, the leading finite-friction correction to the quantum Smoluchowski equation is derived, for the particular case of the overdamped harmonic oscillator. It is in fact a quantum correction, different from the well-known classical correction, and it dominates the classical correction in the strong friction regime.